b2_106_2012 (1)

Upload: insaf-mohamed

Post on 02-Mar-2018

218 views

Category:

Documents


0 download

TRANSCRIPT

  • 7/26/2019 b2_106_2012 (1)

    1/10

    http://www.cigre.org B2 - 106

    SESSION 2012

    [email protected] 1

    Area-wide dynamic line ratings based on weather measurements

    R. PUFFER1)

    ,M. SCHMALE2)

    , B. RUSEK3)

    , C. NEUMANN3)

    , M. SCHEUFEN1)

    1)RWTH Aachen University, Aachen, Germany, [email protected]

    2)TenneT TSO GmbH, Bayreuth, Germany,3)

    Amprion GmbH, Dortmund, Germany

    SUMMARY

    The load of overhead lines has increased due to raised transmission of electrical energy within Europe

    as well as in the consequence of a growing feed-in from regenerative energy resources. The transmis-

    sion capacities of overhead lines (OHL) are limited and already in many cases the bottlenecks which

    restrict the power flows.

    Dynamic rating is a measure to increase the ampacity of overhead lines depending on the actual

    weather situation.

    In the first section this paper focuses on the description and evaluation of different methods and toolsfor OHL ampacity determination. The conductor temperature is measured directly with a sensor as

    well as determined indirectly using a weather station close to the line and commercially available

    weather data. Different scenarios where the measured wind speed is higher than the wind at the line

    due to shadowing effects are taken into account. The results show that the conductor temperature de-

    termination from weather data may be done with a maximal adequacy of about 5 K in the conductor

    temperature range up to 50C. This fact means that the dynamic line rating is applicable but some

    safety margins have to be implemented. It is also shown that investigations on the thermal behaviour

    at low wind speeds seem to be necessary.

    In the second section the focus is on the implementation of a dynamic rating system into the 380 kV

    transmission grid and the necessary measures to increase the ampacity up to 3,150 A. This dynamic

    rating system uses the ambient temperature and the wind speed to determine the dynamic ampacity of

    the line. Retrofitting in substations such as replacing circuit breakers and current transformers as wellas measures at overhead lines such as inspecting joints and raising towers had to be taken. Dynamic

    aspects of the transmission system are discussed. The protection concept was revised in order to allow

    a quick location of faults even in the case of a single technical component failure. The operational

    experience using the dynamic rating system proves that it fits very well with the existing control cen-

    tres technology. The distinct increase in dynamic current rating compared to static rating verifies the

    technical and economical capability.

    KEYWORDSAmpacity, monitoring system, up rate, overhead line, thermal limit, meteorological data, real time

    thermal rating, dynamic rating

  • 7/26/2019 b2_106_2012 (1)

    2/10

    [email protected] 2

    1. IntroductionTo enable the ongoing connection of regenerative energy sources in a timely manner, there is a need

    for flexible measures to better utilise the existing transmission grid. One of those measures is dynamic

    rating of overhead lines. Based on the thermal balance of the conductor it can be determined that the

    meteorological conditions (wind speed, angle of oncoming flow of wind and ambient air temperature)

    affect the temperature of the line conductors considerably. With certain combinations of these mete-

    orological factors, the influence results in a cooling effect, thus much more heat caused by the current

    flow can be generated without exceeding the maximum operating temperature. This means, that an

    overhead line can be loaded more intensively (above nominal current). This effect can also be used for

    a temporary increase of the line capacity (dynamic line rating). Thus it is possible to increase the am-

    pacity of the line and at the same time to maintain the maximum allowable values for the conductor

    temperature and the clearance to ground or objects.

    This paper is divided into two main parts. The first section focuses on the methods for determination

    of the conductor ampacity. For this purpose, the three methods (one direct and two indirect) will be

    compared in terms of adequacy. The second section focuses on the measures necessary to enable a

    retrofitting of existing 380 kV overhead lines in order to prepare them for dynamic rating. The most

    significant among these measures were the introduction of dynamic rating, essential actions in the

    overhead line sections like rising towers and inspection and replacement of primary technical equip-ment in the substations. Further the ampacity increases of OHL operated with dynamic rating are pre-

    sented.

    2. Comparison of methods for ampacity determination

    2.1 Principal methods and toolsFor dynamic line rating, the conductor temperature can be used. The interesting questions are how to

    acquire the temperature, which adequacy is necessary and which monitoring system is the most suit-

    able from the economical point of view. In order to answer these questions, a pilot installation of two

    monitoring systems at Amprion GmbH (German TSO) was established (figure 1).

    The first system measures directly the temperature of

    the conductor by means of two passive surfaceacoustic wave (SAW) sensors SAW 1 and SAW 2

    located in two conductors of one circuit. The second

    system (ls - local station) bases on an indirect method

    using a thermal model for the calculation of conduc-

    tor temperature under consideration of the meteoro-

    logical conditions. In this case, a weather station is

    placed in the vicinity of the conductor.

    The cost of the pilot systems and the technical effort

    was quite high. Taking into account the actual costs

    of the measuring devices, the effort for the installa-

    tion and the necessary line outages the installation of

    such systems throughout the network is not economi-

    cal. The application of weather stations similar to (ls) does not require de-energising of the line and the

    installation cost expenditure is significantly lower. However, the necessity to equip all lines with

    weather stations still remains. The simplest solution is to use already available weather stations, which

    are located in the vicinity of the monitored line, and to project the measured meteorological conditions

    on the line. Therefore, the pilot project was extended by an additional indirect method (rs - remote

    station) which calculates the conductor temperature using the commercially available meteorological

    data.

    The aims of the project are to define the adequacy of conductor temperature determination from the

    meteorological data, provided by the local and remote weather station and to find the most suitable

    system from economical point of view.

    Fig. 1 Pilot installation of monitoring systems

    with SAW sensors and local weather station

  • 7/26/2019 b2_106_2012 (1)

    3/10

    [email protected] 3

    2.2 The thermal model of the conductorFor the indirect method the CIGRE-thermal model of conductor

    [2] is used. The principle of the model is well known; the ther-

    mal balance of the line, i. e. introduced heat and dissipated heat,

    must be equal at any time (equation 1).

    nckcrscmcj PTPTPPPPTP ++=+++ )()()( (1)

    where : Pj- current losses, Pm magnetisation losses, Ps-solar radiation,

    Pc- corona losses; Pk - convection, Pn rain, Pr radiation

    Knowing the weather conditions and some constant conductor

    parameters, the ampacity at which the conductor reaches its

    maximum permissible temperature (in this case 80C) which also

    corresponds to the maximum permissible conductor sag can be

    calculated according to equation 1 (see also figure 2).

    The calculation of conductor temperature based on the load cur-

    rent and the weather conditions is quite complex, because of

    numerous dependencies on the conductor temperature itself. The direct derivation of conductor tem-perature (with a few simplifications) is possible [7]. This equation may also be solved by an iterative

    approach (figure 2). The temperature of the conductor (Tc) will be varied until both sides of equa-

    tion (1) are almost equal (error < 0.1C).

    2.3 Statistical approachThe investigations cover almost 2 year of measurements almost 50,000 data sets with 15 min resolu-

    tion. The most suitable approach for analysis of such amount of data is a statistical approach [8].

    Hence in this work, the relative frequency of different parameters [11] will be applied.

    From this statistical evaluation given in figure 3 it can be derived for both sensors SAW 1 and SAW 2

    that the conductor temperatures were lower than 10C in 30% of time period considered and for 10%

    of time period considered higher than 30C. This shows that the conductor temperatures are far below

    the permissible limit of 80C and that there is a potential for increasing the ampacity which can beutilised by overhead line monitoring.

    2.4 Shadowing scenariosThe weather conditions which are measured by

    local and remote weather stations give infor-

    mation about the condition in this particular

    location [8][9]. Since the overhead lines may

    be many kilometres long, the weather condi-

    tions along the line will not be the same and

    particularly affected by different wind speeds

    and directions. Additionally, a shadowing ef-

    fect has to be taken into account, if the line

    passes valleys or forest aisles [10].

    Therefore, four scenarios with varying wind

    speed and direction will be considered to simu-

    late shadowing effects (table 1). The principle

    of application of shadowing effect is shown in

    figure 2.

    2.5 Measured conductor temperatures and possible ampacitiesIn the considered period of time a variety of different weather and load conditions have been meas-

    ured. The conductor temperatures varied between -10 and 50C and the load current between 0 and

    100% of conductor nominal current (figure 3). That means that the complete current range was cov-ered, but the maximum conductor temperature of 80C was not reached.

    sce-

    nario

    wind speed wind direc-

    tion

    S1 v = 0.6 m/s = 90

    S2 v = vreal/2 &

    min(v) = 0.6 m/s

    = real&

    min() = 30

    S3 v = vreal/2 &

    min(v) = 0.6 m/s

    = 30

    S4 no restrictions = real&

    min() = 30

    Tab. 1: Different shadowing scenarios, where vreal is

    the measured wind speed an v is the wind speed used

    for ampacity calculation

    Fig. 2 Principle of calculation of

    ampacity @ maximal conductor

    temperature and conductor tem-

    perature @ known load current

  • 7/26/2019 b2_106_2012 (1)

    4/10

    [email protected] 4

    Fig. 3: Measured conductor temperature (A) and currents of the monitored overhead line (B)

    2.6 Discussion of resultsThe two sensors of the conductor temperature measuring system (SAW 1 and SAW 2) are mounted on

    two conductors of the same circuit, but at different heights. Due to the phase arrangement of the circuit

    on the tower, sensor SAW 2 on conductor 2 is mounted about 3 meters higher than sensor SAW 1 on

    conductor 1. The wind profile and herewith the cooling effect is depending on the height aboveground. Thus the cooling of the higher located conductor 2 should be more intensive than the cooling

    of conductor 1. The resulting conductor temperatures should differ. This dependency on wind condi-

    tions can be seen in figure 4, curve (1). The positive deviations from T c_saw1 show that for 90% of

    considered period the temperature of the lower conductor is few degrees higher. Since the temperature

    Tc_saw1 is higher than Tc_saw2, the conductor sag of conductor 1 will be larger than of conductor 2.

    Therefore, the temperature of the conductor 1 (Tc_saw1) will be chosen as reference value.

    The temperature of the conductor (Tc) is calculated using CIGRE-model and different shadowing sce-

    narios. The weather conditions are measured by local weather station (ls) and remote weather station

    (rs). The difference between calculated conductor temperatures (M2 and M3) and directly measured

    conductor temperature (M1) is shown in figure 4. The cumulative frequency distribution of these de-

    viations for exemplary study cases is also shown.

    The curves in figure 4 can be analysed as follows:

    Positive deviations mean that measured conductor temperature (Tc_saw1) is higher than the

    calculated temperature. This condition implies a risk to exceed the maximum allowed conduc-tor temperature.

    Fig. 4: Frequency of differences between measured and calculated conductor temperature for different

    shadowing scenarios depending on the location of weather station (ls-local, rs-remote)

  • 7/26/2019 b2_106_2012 (1)

    5/10

    [email protected] 5

    Negative deviations are allowed, since the conductor temperature is in the permissible range.In this case, the maximal ampacity will not be reached in any case.

    Scenario S1 (only temperature, curve (8): This scenario gives the best adequacy because only1% of deviations is higher than 5C. However, it does not utilise the maximum of conductor

    ampacity, because 80% of deviations are negative. Interesting is, that the use of ambient tem-

    perature and standard normative weather conditions (v = 0.6 m/s, = 90) still produces posi-tive deviations in 20% of data points. Hence, it can be concluded that either there are worseweather conditions than those in standard or the models are not good enough at those small

    wind speeds. This fact requires further investigations.

    Scenario S2, (half wind speed, = real& min()=30, curves (6) & (7)): This scenario appliesthe real wind direction in the model, in contrary to scenario S3 at which a constant angle of

    wind direction is used. It is well to be seen in particular, if the curves for local station (5) and

    (7) are compared. The positive deviations are almost equal to the use of temperature only

    (scenario S1). The method provides a very good safety margin. Hence, the distribution curve

    for a local station is very narrow and the scenario has a good safety margin, this location of

    the weather station and this shadowing scenario give the best representation of the conductor

    temperature.

    Scenario S3 (half wind speed, = 30, curves (4) and (5)): For the local station there are about50% of positive deviations and for the remote station slightly less than 40%. However, only

    about 5% of deviations are higher than 5C. On the negative side of axis the calculations ac-

    cording to data from remote station exhibits much more inadequacy than for data coming from

    local station.

    Scenario S4 (wind speed with no restrictions, curves (2) and (3)): Almost 80% of deviationsare positive. However, only 10% of deviations are higher than 5C. Here, the calculated tem-

    perature is lower than the measured one. The direct use of wind speed with no restrictions for

    calculation of conductor temperature is apparently not adequate enough. The local weather

    station is located at a similar height above ground as the conductor; therefore it should provide

    comparable results. The reason for this effect which mainly appears at low wind speeds (see

    figure 5A) may occur due to inadequacy in weather measurements, the conductor models

    and/or dynamic thermal behaviour of conductor. Moreover, the sensors measuring the tem-perature directly are calibrated for wind speeds in range of 4 m/s and may produce small de-

    viations at low wind speeds.

    According to discussion above, the scenario S2 is the most accurate for ampacity determination. But

    the results also show that there is no method which can determine the conductor temperature very

    exactly. In case of ls_S2 (local weather, half wind speed, and taking into account wind directions) a

    deviation of 5 C may be reached. It has to be mentioned here, that this deviation refers only to the

    conductor temperatures up to 50C. Above this value, no observations have been made.

  • 7/26/2019 b2_106_2012 (1)

    6/10

    [email protected] 6

    Fig 5: Deviations of theoretically calculated conductor temperature to the measured conductor temperature

    dependent of the wind speed (A), ambient temperature (B) and the season of the year (C)

    The dependency of the deviations between measured conductor temperature and calculated tempera-

    ture using the local and the remote weather conditions at scenario 2 is shown in figure 5.

    At higher wind speeds the deviations become smaller (figure 5A). The dependency on the ambient

    temperature (figure 5B) cannot be detected at the first look. The dependency on the season of the year

    (figure 5C) is also difficult to recognise. Obviously the largest deviations occur within few days (peaks

    in figure 5C) and at ambient temperatures of about 10C (peak in figure 5B). For clarification of thesedetails further investigations are needed.

    3. Area-wide dynamic rating of 380 kV overhead linesAn important north to south connection in the

    German grid of TenneT TSO GmbH is located

    between the cities of Hamburg and Frankfurt (see

    figure 6). To adjust the grid to the new boundary

    conditions it is necessary to build new lines as

    well as to improve the efficiency of the existing

    infrastructure. The policy is to fully utilise the

    existing infrastructure first and to have new lineserected only for further demand.

    An overview of the necessary measures to be

    taken in order to increase the transmission capabil-

    ity of this part of the grid is given in figure 7.

    In the 380 kV transmission grid it is essential to

    keep up the stability of the system. By raising the

    maximum allowable ampacities the development

    of a new protection concept became necessary.

    Also a concept to maintain system safety for

    higher utilisation was required. As a result facili-

    ties providing reactive power had to be installed

    and changes to the protection system were carried

    out.

    50HertzTransmission

    Amprion

    Sweden

    SvenskaKraftnt

    Denmark

    Energienet.dk

    Hamburg

    Frankfurt

    EnBW

    Netherlands

    TenneT

    Czech Republic

    CEPS

    AustriaTIWAG

    APG

    50HertzTransmission

    Amprion

    Sweden

    SvenskaKraftnt

    Denmark

    Energienet.dk

    Hamburg

    Frankfurt

    EnBW

    Netherlands

    TenneT

    Czech Republic

    CEPS

    AustriaTIWAG

    APG

    Fig. 6: Retrofitted connection between Ham-burg and Frankfurt

  • 7/26/2019 b2_106_2012 (1)

    7/10

    [email protected] 7

    yes

    overhead linedynamic rating

    applicable

    no

    documentation

    everythingdone?

    noOK?

    yes

    noOK?

    yes

    noOK?

    noOK?

    noOK?

    noOK?

    yes

    yes

    yes

    yes

    implementation of ampacity algorithm

    weather station and location

    check design temperature

    check joints

    replace

    replace

    replace

    adapt, replace

    adapt max. ampacity

    check substation

    check protection anddynamic aspects

    magnetic field threshold

    increase design temp.

    special inspection

    Fig. 7: Workflow of necessary measures for dynamic rating implementation

    3.1 Dynamic aspects of the transmission systemThe transmission capacity is increased by raising the ampacity of the 380 kV bottleneck circuits to

    3,150 A. With an increasing utilisation of the currently existing connections without adding new

    transport capabilities from the north to the south, the risk of loosing the generator stability (phase an-

    gle stability) increases as well (see figure 8).

    The stability limits mainly depend on the grid impedances (inductive and capacitive). Also the protec-

    tion system is affected by high nominal currents, in regard to selectivity and reliability. It is more dif-

    ficult to safely detect and isolate faults. High nominal currents make it hard to differentiate between

    operational and fault currents without the chance of incorrect tripping.

    To improve the transport capacity of the grid the system boundaries which arise from system stability

    and grid protection have to be taken into account during the grid planning process. Analysing the pos-

    sibilities of enhancing the capacity of the main transmission corridors from north to south system

    many studies were conducted. As a part of the EWIS study (European Wind Integration Study) the

    results were verified in an European context, considering coordinated robust scenarios (European

    market model for power plant operation) and measures (e. g. the grids at the borders to the Czech Re-public, Poland, Austria, Benelux or Denmark).

    0 45 90 135 180bertragungswinkel

    P

    0 45 90 135 180bertragungswinkel

    P

    = sin

    X

    UUP 212

    staticboundary

    P1 withoutexpansionoftransmission system

    instablestable

    PDLR

    with expansionoftransmission system

    increasing

    transmission capacity

    reduction oftransmission angle

    transmission angle Fig. 8: transmission angle as a function of the transmission capacity (DLR Dynamic Line Rating)Where P1is the feeding power and P2is the load power, PDLRis the increased feeding power using dynamic line rating,

    U1and U2are the voltages at the beginning and the end of the line, and is the angle between current and voltage

  • 7/26/2019 b2_106_2012 (1)

    8/10

    [email protected] 8

    3.2 Protection of the transmission systemThe protection concept was revised in order to allow a quick location of faults even in the case of a

    single technical component failure. The analysis of the calibration principles of the protection system

    revealed that raising the boundary protection current and accordingly a less sensitive tripping setting

    on its own was not sufficient to meet the increased requirements. In addition the influence of large

    transmission angles on the measuring precision of the distance relays in the event of electric ark faults

    and compensation currents in healthy lines at a single line fault are factors of consideration.

    3.3 Realization of necessary measuresThe ampacity of a high voltage circuit can be limited by the primary equipment in the substation bays

    and by the overhead lines. The equipment used in the substation bays can generally be retrofitted to

    match the ampacity that can be achieved using the dynamic rating of the line. In order to determine

    presently available ampacity, the weather data has been evaluated. This evaluation shows that in about

    80 % of the year a weather dependent ampacity of 3,150 A is possible (see figure 9).

    3.4 Measures in substationsIn the substations the following primary equipment has been reviewed and replaced as needed:

    circuit breaker

    current transformer

    isolating switch

    voltage transformer switch bay lines

    For the circuit breaker, current transformer, isolating switch and for some voltage transformers (spe-

    cial types) the rated currents were checked. For equipment with thermal ratings below 3,150 A, the

    device had to be replaced.

    The switch bay lines and bus bars were checked in regard to their short circuit capability. Insuffi-

    ciently dimensioned components have been replaced.

    The above mentioned measures took a great amount of planning and coordination because of the lim-

    ited operability of the grid during the intervention and the aim not to cause any impact on customers.

    1,000

    2,000

    3,000

    4,000

    5,000

    0 10 20 30 40 50 60 70 80 90 100

    time [%]

    w

    eatherdependentampacity[A]

    3,150 A

    4,000 A

    2,500 A

    2,000 A

    four bundle conductor ACSR 240/40: 2,580 A

    Fig. 9: Available ampacity with dynamic rating of the connection between Hamburg and Frankfurt

  • 7/26/2019 b2_106_2012 (1)

    9/10

    [email protected] 9

    3.5 Measures at overhead linesSince the usable ampacity of an overhead line depends among other things on the specific design tem-

    perature, generally the ampacity can be increased by raising the clearance. If the specific design tem-

    perature of lines is lower than the rated conductor temperature an ampacity increase can usually be

    reached by the elevation of selected towers. However, the elevation of a 380 kV line tower yields a

    couple of challenges. For example, in order to elevate a 10 ton tower, special cranes are needed which

    have to approach the tower if necessary over provisional tracks (figure 10).

    Fig. 10: Pictures of inserting additional body sections in a 380 kV tower near Stade

    The joints in the line section were completely inspected on site. Only intact connection components

    remained in the line whereas conspicuous components were replaced. The condition of joints was de-

    termined using infra-red thermography.

    Raising the ampacity of an overhead line raises the maximum value of the magnetic field as well. Cal-

    culations of the magnetic field were carried out in order to assure the compliance with legal specifica-

    tions.

    3.6 Implementation of dynamic rating into the operating system

    In order to improve the ampacity of 380 kV lines a dynamic rating system has been developed andimplemented into the existing operating system of TenneT TSO in Germany. This monitoring system

    uses the ambient temperature and the wind speed to determine the dynamic current rating of the line. It

    is directly linked to the control centre and delivers a dynamic current rating. There is no need for any

    direct measurement of the conductor temperature to determine the dynamic current rating.

    The operational experience using the dynamic rating system for the operation of 380 kV lines proves

    that it interposes very well with the existing control centres technology. The distinct increase in dy-

    namic current rating compared to static rating verifies the technical and economical capability.

  • 7/26/2019 b2_106_2012 (1)

    10/10

    [email protected] 10

    4. ConclusionMany overhead line monitoring systems (direct and indirect temperature determination methods) are

    presently available on the market. The determination of conductor temperature using weather data is

    riddled with many inadequacies.

    Hence, the conductor temperature determination from weather data may be done with a maximal ade-

    quacy of about 5 K in the conductor temperature range up to 50C.

    The findings of this paper show that the accuracy of indirect monitoring systems is comparable with

    direct monitoring systems considering adequate safety margins. Moreover, investigations on the ther-

    mal behaviour at low wind speeds seem to be necessary as well as better understanding at what time

    the largest deviations to the measured conductor temperature occur.

    A dynamic rating system using weather measured in substations to calculate the ampacity was in-

    stalled on 800 km of 380 kV overhead lines. Different retrofitting measures like checking the joints,

    changing substation equipment, raising towers and verifying the stability criteria of the grid had to be

    done.

    The operational experience using the dynamic rating system delivers a distinct increase in dynamic

    current rating which verifies the technical and economical capability of the system.

    BIBLIOGRAPHY

    [1] Drger, H.-J.; Hussels, D.; Puffer, R.; Development and Implementation of a Monitoring-

    System to Increase the Capacity of Overhead Lines, Paper B2-101, Cigr Session 2008

    [2] Cigr, Technical Brochure 207; The Thermal Behaviour of Overhead conductors, August 2002

    [3] H. Khn, F. Martin, M. Schmale, R. Puffer, W. Winter; Mehr Energie von Nord nach Sd, ew

    3/2011 and 4/2011

    [4] M. Schmale, R. Puffer; Freileitungen sicher betreiben und Reserven nutzen, netzpraxis, Jg. 49

    (2010), Heft 11

    [5] Blumenroth, F., Lbl, H., Gromann, S., Puffer, R. Hussels, D.: Ageing of high current joints in

    power transmission ans distribution systems, Cired 2007, paper 537

    [6] Schmale, M.; Puffer, R.; Drger, H.-J.; Experience with a Dynamic Rating System to Increasethe Ampacity of 380-kV Overhead Lines, Cigr Symposium Bologna 2011

    [7] Teminova, R.; Hinrichsen, V.; Freese, J.; Hudasch, M.; Bebensee, R.; Neumann, C.:

    Betriebserfahrungen mit passiven funkabfragbaren OFW-Sensoren zur Messung der Temperatur

    von Freileitungsleiterseilen und Trennschalterkontakten, ETG Tagung, 2006

    [8] Lange, M.; Focken, U.: Studie zur Abschtzung der Netzkapazitt in Mitteldeutschland in Wet-

    terlagen mit hoher Windeinspeisung, Studie energy & meteo systems, Oldenburg, 2008; gefr-

    dert vom BMU

    [9] Roman, H. Dangrie, G.; Darendorf, S. Struck, T.: Freileitungsmonitoring im Hochspannungs-

    netz - Theoretisches Potenzial. ew Jg. 108 (2009), Heft 12, S. 62-66

    [10] Roman, H. Dangrie, G.;Darendorf, S. Struck, T.: Freileitungsmonitoring im Hochspannungs-

    netz - Reales Potenzial. ew Jg. 108 (2009), Heft 13, S. 60-63

    [11] Neumann, C.; Rusek, B.; Puffer, R.: Weather dependent loading of overhead lines based on

    statistical consideration of weather data (in German). ETG Congress, Duesseldorf, 27. to 28.

    October 2009, Report 3-7