Recent Articles and Newsletters


Some Simple Line Rating Theory
We have received questions specifically relating to line rating calculations. This newsletter attempts to provide some of the high level theory behind conductor rating calculations.

Short Time Line Ratings
This newsletter examines the potential for manual switching to secure load under N-1 conditions. Our systems calculate the 10 minute jump overload capability.

Fault Current Rating of Conductors
This newsletter describes some of the considerations associated with fault current rating calculations. A complimentary calculation tool is provided here

Implications of Load Encroachment on Line Ratings
The allowable transmission line rating is dictated by the point at which the load impedance intersects with the relay characteristic. A complimentary calculation tool is provided here.

Impact of Magnetic and Electric Fields
This newsletter discusses some of the issues which need to be considered when assessing the compliance with allowable magnetic and electric field thresholds. Calculation tools are available here.

Conductor Ratings on Hot Days
This article reviews the rating performance of an ACSR/GZ 54/7/3.50 conductor when the ambient temperature exceeds 40 degrees Celsius.

What are Reliability Criteria?
This newsletter reviews the probabilistic nature of the reliability criteria commonly used for planning purposes and demonstrates how financial savings can be made.






Some Simple Line Rating Theory

The Need for Thermodynamics

If you have completed an engineering degree, you probably encountered Thermodynamics during an early university subject. If you are an electrical engineer, you probably also remember forgetting most of this new knowledge at the end of the session! However, the rating of overhead lines requires a basic understanding in this esoteric art as the rating of a line is often restricted by the allowable conductor temperature. This restriction can be imposed due to the need to maintain ground clearances or to protect the conductor from permanent damage due to heat. Calculating the conductor temperature requires an understanding of the heat sources and the flow of heat to the surroundings.


SOURCES OF HEAT GENERATION:

  • EFFECTS OF SOLAR RADIATION
  • THE INTERNAL RESISTANCE OF THE CONDUCTOR

PREDOMINANT HEAT SINKS:

  • RADIATION FROM THE CONDUCTOR SURFACE
  • THE EFFECTIVE CONVECTION PROVIDED BY THE MOVEMENT OF AIR

The continuous current rating occurs when the line is operating at its maximum allowable temperature and the heating effects match the cooling effects.


Heating due to Solar Radiation

WeatheRate has implemented the Australian guidelines [1], where solar radiation is calculated from equations which define the location of the sun in the sky. These equations require the latitude and longitude of the line span, as well as the time of day and month of the year. From the route and type of line conductors, it is then possible to accurately determine the solar heating imposed on the phase conductors.

Direct measurement of the solar radiation is usually avoided due to the added expense associated with omnidirectional radiation transducers. Moreover, the presence of cloud often means that solar radiation measurements cannot be applied at distances from the measurement location.


WeatheRate also provides the option to utilise the equations in [2], which assumes a constant solar radiation during the day.


Heating due to Conductor Resistance

Manufacturers need to ensure that their conductors have a dc resistance no greater than the values stipulated in [3, 4, 5]. The subsequent calculation of ac resistance includes factors for the skin effect, operating temperature, the external proximity effect and axial effects caused by helically stranded conductors. The proximity effect is generally negligible at power frequencies on overhead lines, and may be ignored. Similarly, the axial effects of helically stranded conductors have historically been accounted for through magnetic coefficients that are applied to the conductor resistance.

In recent years, more accurate calculations have been developed in [6] and [7], which account for the lay length and current dependent nature of the Rac/Rdc ratio. This relationship has now been considered in the Australian TNSP line rating calculations [1]. Consequently, it is possible to accurately define the resistive heating introduced by the ampere loading on the line.


Cooling due to Radiation

If you’ve managed to remember Stefan-Boltzmann Law of Thermodynamics, you will probably also remember that calculated irradiation is a function of the 4th power difference in temperature. For rating calculations, the radiation is calculated using a simplification that includes the difference between the conductor temperature and both the sky and ground temperatures. Since the conductors act as a ‘grey body’, it is also necessary to include the conductor emissivity in this calculation.


For instance, the following diagram shows the relationship which exists between the conductor temperature and the radiative heat emission for various conductors under daytime conditions.


Cooling due to Convection

Heat is also extracted from the conductor through convective cooling. The conductor is cooled through natural convection when there is no wind and forced convection when there is a strong transverse wind to the conductor. WeatheRate utilises equations [1] that provide a smooth transition between these two cooling methods, where this is achieved through ...

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Short Time Line Ratings

Short-time transmission line rating calculations can provide significant flexibility when transferring loads between bulk supply points or when subsystems operate in parallel with main system transmission lines. These benefits arise from the use of our ten minute short time rating calculations which are generally 30 to 40% higher than the continuous line rating.


Consider a 33kV substation E which is normally supplied from sub-transmission substation C via two 33kV feeders. These feeders are rated at 42 and 56 MVA respectively, while the demand of substation E presently peaks at 50 MVA in summer.


The network service provider needs to consider the potential loading introduced by an outage of the main grid line when initiating 33kV load transfers between the bulk supply points. The loading on these 33kV lines are primarily affected by the voltage angles at the two main grid (275 or 330kV) busbars. For a short main grid line, these angles are commonly assessed from the following equation.



Even larger flows will be seen following a trip of this line. Consequently, the 42 MVA feeder between substations D and E is normally left out of service due to the high loading that would occur on this tie connection if the main grid line tripped.


When normally supplied from substation A, the 1% load duration at substation E will exceed the firm rating of the two in service feeders this coming summer. As a result, it is assumed that a project has been initiated to increase the rating of both feeders between substations C and E to 56 MVA. Interestingly, this project may be deferred or even cancelled by placing the third feeder in service and utilising its short-time rating capability.


Short-time calculations can also provide flexibility at distribution voltages. Most distribution feeders are ...

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Fault Current Ratings

The continuous and short-time ratings of an overhead conductor are often determined by a design temperature above which the conductor reaches an allowable clearance to ground. However, in many situations it is possible to utilise a maximum conductor temperature which exceeds the actual design temperature of a transmission line. For instance, it is possible to utilise a smaller conductor for dropper connections into substations or higher temperatures for spans where there are no ground clearance issues. Nevertheless, the use of smaller conductors can introduce fault rating limitations which need to be assessed and catered for in the design process.


Fault ratings are generally derived from an assessment of the mechanical forces and the thermal heating which can occur within the conductor. The thermal heating is often assessed using lookup tables which describe the allowable energy dissipation as I2t values. These tables provide information which is based on assumptions, such as the initial temperature and the maximum allowable temperature, as well as a static conductor resistance. Moreover, these tables often overlook the influence of magnetic heating which can occur within some ACSR conductors. This magnetic heating is more pronounced when there is one outer layer of aluminium, but is also present when there are three layers. Since the resistance and magnetic heating are respectively a function of the temperature and conductor current, it is not generally possible to derive a simple energy dissipation I2t value.


Rather, the more accurate approach requires an iterative calculation to determine the temperature rise over a small interval of time. This new temperature is used to calculate the conductor resistance, and is subsequently used to derive the conductor temperature following the next interval of time. The heating effects of conductors are described by the equations in [1], but reference should also be given to the adiabatic heating process described in [2]. It is therefore possible to derive the allowable clearing times for various values of current on the assumption that no net heat transfer occurs between the conductor and its surroundings. For example, the following diagram shows the maximum fault current operating limit curves for several overhead conductors where the initial conductor temperature is 50 Deg Celsius and the upper temperature limit is 200 Deg Celsius.


These fault rating calculations are very important when designing earthing systems, as well as for supported overhead phase conductors, such as substation droppers, sections of strung busbar, or even 11 and 22 kV distribution circuits near zone substations. Similarly, the calculations are necessary when maintaining compliance with critical clearance times or even when designing heating elements such as braking loads for transmission networks. However, it should be noted that decrement factors may need to be applied where the X/R ratio of the source impedance is high. More information on decrement factors is available in

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Implications of Load Encroachment on Line Ratings

Protection limitations are often overlooked when defining transmission line ratings due to the increasing use of unit protection (current differential) schemes. However, distance protection is still employed on many transmission circuits, and is commonly used as a backup protection within sub-transmission systems. The application of distance protection schemes can limit the allowable line current if the load (and power factor) begins to encroach on the relay characteristic.


Several distance relay characteristics have been employed in recent years. The most common of these include the offset mho, quadrilateral and lenticular relay characteristics, as shown below. In each case, the allowable transmission line rating is dictated by the point at which the load impedance intersects with the relay characteristic.


Interestingly, load encroachment has been one of the primary factors associated with the North American blackout (14th August 2003), the European disturbance (4th November 2006) and the recent Indian blackouts (30-31st July 2012).


The North American blackout resulted in the loss of more than 70,000 MW of load in the country’s north-east. The event was initiated by the tripping of a few transmission lines in the network. This resulted in higher loads being applied to the remaining transmission lines; many of which were subsequently tripped by zone 3 protection impedance relays. This issue was exacerbated by the low voltage levels and high reactive power flows.


The European event was initiated from the manual opening of a double-circuit 380 kV transmission line. This produced high loads on another 380 kV line, where the load was very close to the protection settings. A small power flow deviation subsequently triggered a cascade of line tripping events which resulted in frequency-based load shedding.


The recent Indian blackouts occurred on two consecutive days. In each case, the loss of load was initiated by the tripping of a 400 kV transmission line due to the encroachment with a zone 3 distance protection element. Subsequent load encroachment issues resulted

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Impact of Magnetic Fields

Magnetic fields are commonly discussed during the design phases of transmission line construction. Several studies have tried to assess the biological effects of electromagnetic fields. These have included in vitro (single cell), in vivo (studies on animals) and epidemiological (statistical) and specific occupational studies [9]. Several researchers have also combined all the epidemiological studies for specific symptoms or diseases, in a process known as meta-analysis. Some studies claim to have found a statistically significant correlation between magnetic fields and heath issues when the line voltage is greater than 100 kV [9].


In response to such research, the National Health and Medical Research Council released some interim guidelines in 1989. These recommended a limit for the general public of 1,000 mG for full-time exposure to magnetic fields or 10,000 mG for occasional exposure. These values were effectively superseded by the Australian Radiation Protection and Nuclear Safety Agency, who issued a draft standard in 2006. This reiterated the limit of 1,000 mG due to an assessment of the instantaneous rms electric field induced within the body, averaged over a volume of tissue. The International Commission on Non-Ionizing Radiation Protection has subsequently published guidelines, which stipulate an allowable magnetic field for public exposure of 2,000 mG, where “the main interaction of magnetic fields is the Faraday induction of electric fields and associated currents in the tissues” [4].


The law of Biot-Savart describes the magnetic field observed adjacent to a section of current carrying conductor [10]. This can be used to provide a good mathematical representation of the rms magnetic field associated with three phase transmission lines. The resultant fields are derived from the magnitude of the ac line current and the transmission line construction and phasing [6]. For instance, the following diagram shows a hypothetical double circuit 132 kV transmission line, which has low reactance and high reactance phasing. A phase current of 500A is applied to each circuit, where the phase conductors are AAAC 1120 Oxygen (19/4.75) and the height of centre phase is 11.25m.



The phase current used in magnetic field calculations should be derived from detailed load flow modelling to derive a forecast load duration curve for the line. The load which is exceeded for no more than 15% of the time is then

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The impact of magnetic fields were discussed in our last newsletter. This noted that the allowable magnetic field for public exposure is generally considered to be 2,000 mG and that the compliance calculations require detailed load flow modelling to derive a forecast load duration curve for the line.


Electric fields are less commonly considered when designing transmission lines at voltages below 275 kV. However, this issue is receiving more attention when reviewing the compliance of existing lines as some designs were previously completed using a 10 kV/m criterion.


As noted in our last newsletter, the National Health and Medical Research Council released interim guidelines in 1989. These recommended a limit of 5 kV/m (rms) where the general public might reasonably be expected to spend a substantial part of day. Exposure to fields between 5 and 10 kV/m were to be limited to a few hours per day. These values were effectively superseded by the Australian Radiation Protection and Nuclear Safety Agency, who issued a draft standard in 2006. This reiterated the limit of 5 kV/m at 50 Hz but did not provide any compatibility for fields in excess of this threshold. The International Commission on Non-Ionizing Radiation Protection has subsequently published guidelines, which stipulate an allowable electric field for public exposure of 5 kV/m at 50 Hz, where the main interaction is the induced oscillating charges on the surface of the exposed body and the currents they produce within the body.


The electric field at ground level is closely related to the charge on each conductor of the transmission line. Unfortunately it is not possible to directly calculate the charge on the conductors of a multi-phase line directly from the positive sequence capacitance without also considering the matrix of Maxwell potential coefficients and the interactions between each conductor. Consequently, for a three phase circuit, the charges on the conductors are determined from the known phase voltages and the Maxwell potential matrix.


The resulting fields are derived from the operating voltage and the transmission line construction and phasing. For instance, the following diagram shows the hypothetical double circuit 132 kV transmission line described in our last newsletter. In this case, the phase conductors are AAAC 1120 Oxygen (19/4.75) and the height of centre phase is 11.25m.





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Some of our recent newsletters focussed on the calculation of magnetic and electric fields. In these articles, we noted that circulating current in earthing systems are commonly ignored when assessing the magnetic field adjacent to transmission lines. However, we have received requests to incorporate the effects of circulating currents in earthing systems in our online software.


As shown in the following diagram, the earthing systems of an overhead line (or underground cable) are closely coupled with the primary phase conductors. As a result, significantly large circulating currents can be induced into these earthing systems due to the low impedance of substation earth mats and the tower footings, which are commonly less than 0.1 and 10 ohms, respectively.



These circulating currents can affect the magnitude of the magnetic field under each individual span. For instance, consider the hypothetical double circuit 132 kV transmission line described in our last newsletter. These short lines are constructed using high reactance phasing. The phase conductors are AAAC 1120 Oxygen (19/4.75) and the height of centre phase is 11.25m. One single SC/GZ 7/3.25 earth wire has also been added at a height of 16m.


When these two lines are each carrying 250 MVA, the earth wire current at the centre of the line is approximately 32A. This analysis is commonly achieved using the Alternative Transients Program (sample files can be downloaded here).


As shown in the following diagram, the inclusion of the earth wire current slightly reduces the magnetic field under the line. This can be useful feature if the calculated fields are close to the allowable thresholds. For this reason, we have now provided this facility in EMFRate for ...

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Conductor Ratings on Hot Days

Our last newsletter focussed on the unusually cool weather seen during the 2012 calendar year in South Eastern Australia. However, over the last few weeks we have seen ambient temperatures exceeding 40 degrees Celsius in almost all of the Australian states.


Interestingly, these temperatures also delivered the nation its hottest official day since records began a century ago. Australia’s national average temperature was reported to reach 40.3 degrees on the 8th January. This prompted the Australian Bureau of Meteorology to add two new colours (deep purple and pink) to extend its previous temperature range on the weather forecasting charts, which had previously been capped at 50 degrees Celsius.


It is a common misunderstanding that overhead transmission lines experience their highest operating temperatures when the ambient temperature is high. Moreover, it is incorrect to assume that a transmission line will approach its ratings when there are high ambient temperatures and a corresponding high demand.


It is true that the ambient temperature affects the rating of a transmission line, but when it comes to the ampacity of a line the predominant factor remains the wind speed. Our previous newsletters have described the correlation that exists between ambient temperature and wind speed, where good wind speeds (and improved ratings) generally occur when there are high ambient temperatures.


As an example of this phenomenon, the following diagram shows the ambient temperature and wind speed recorded at one of our installations in Sydney on the 8th January 2013.



As expected, the wind speeds were relatively low before sunrise, but the wind increased significantly as the high ambient temperatures introduced convective air movements.


It is also interesting to examine the performance of a hypothetical ACSR/GZ 54/7/3.50 conductor with a design temperature of 75 degrees Celsius. The continuous rating of this conductor could have been in excess of 1200 Amps when the highest ambient temperatures were experienced. A ten-minute rating of at least 1400 Amps could have been achieved during the same time frame if the initial line loading was half the calculated continuous rating.


It is particularly interesting to compare these values against the documented summer-noon ratings published by an Australian conductor manufacturer, which are also shown below. This diagram is particularly interesting as it also demonstrates how the ten-minute calculations provide a large improvement over the continuous ratings when the wind speeds, and subsequent ratings, are low.



... Our last newsletter discussed the observations from the 8th January, which was Australia’s hottest official day since records began a century ago. On this day, Australia’s national average temperature reached 40.3 degrees. However, the 18th of January also registered as Sydney’s hottest day since temperature records began. Sydney was reported to reach a maximum temperature of 45.8 degrees, which exceeded the previous record of 45.3 degrees.


Our previous newsletters have described the correlation that exists between ambient temperature and wind speed, where good wind speeds (and improved ratings) generally occur when there are high ambient temperatures. The following diagram shows the ambient temperature and wind speed recorded at one of our installations in Sydney on the 18th January 2013.



As expected, the wind speeds increased significantly as the high ambient temperatures introduced convective air movements. However, it is also interesting to note the impact of the cold front which arrived just after 8pm that evening.


It is also interesting to examine the ...

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... Previous newsletters discussed the line rating observations from the 8th January, which was Australia’s hottest official day since records began a century ago. Analysis from the 18th of January (Sydney’s hottest day on record) also demonstrated that weather measurements can facilitate higher ratings on hot days.


As noted in previous newsletters, it is a common misunderstanding that overhead transmission lines experience their highest operating temperatures when the ambient temperature is high. In reality, there is usually a strong correlation between ambient temperature and wind speed, where good wind speeds (and improved ratings) generally occur when there are high ambient temperatures.

The following diagram shows the ambient temperature and wind speed which was recently recorded at one of our installations in Sydney on the 10th October 2013.


Consider the performance of a hypothetical ACSR/GZ 54/7/3.50 conductor with a design temperature of 75 degrees Celsius. The continuous rating of this conductor could have been in excess of 1200 Amps when the highest ambient temperatures were experienced. The documented summer-noon ratings published by an Australian conductor manufacturer are also shown for comparison.




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... One of our previous newsletters focussed on the rating observations from Australia’s hottest official day since records began. Fortunately, the ambient temperatures during January 2014 were not quite as severe. Nevertheless, we have provided an analysis of the temperatures and ratings observed from Wednesday the 15th January to Saturday the 18th January 2014. These again demonstrate that weather measurements can facilitate higher ratings on hot days.


It is a common misunderstanding that overhead transmission lines experience their highest operating temperatures when the ambient temperature is high. In reality, there is usually a strong correlation between ambient temperature and wind speed, where good wind speeds (and improved ratings) generally occur when there are high ambient temperatures. These wind speeds are often not strong enough to maintain supply from renewable energy sources, but they can facilitate higher than normal ampere ratings on transmission lines.

The following diagram shows the ambient temperature and wind speed which was recently recorded at one of our installations in Sydney between the 15th and 18th of January 2014.


Consider again the performance of a hypothetical ACSR/GZ 54/7/3.50 conductor with a design temperature of 75 degrees Celsius. The continuous rating of this conductor could have been in excess of 1100 Amps when the highest ambient temperatures were experienced.



The documented summer-noon ratings published by an Australian conductor manufacturer are also shown for comparison. It is interesting to note that the continuous rating did approach the summer noon rating (1m/s transverse wind) for a short period of time around midday. However, it should also be noted that the peak substation demand rarely occurs at midday and the 1200A short time ratings could have been used to conduct post-contingent load transfers, if required.


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What are Reliability Criteria?

Networks are generally planned to ensure that firm supply is available during periods of peak demand on the network. This relies on ensuring that load is supplied to an acceptable level of risk.


The National Electricity Rules [1] describes this planning risk as the “firm delivery capacity”, which:


"means the maximum .. load of a network .. under single contingency conditions, including any short term overload capacity having regard to external factors, such as ambient temperature, that may affect the capacity of the network or facility".


More commonly, this firm delivery capacity is defined by the “N-1” capability of the network [2, 3].


"there will be no inadvertent loss of load .. following an outage of a single circuit (a line or a cable) or transformer, during periods of forecast high load."


Each of these definitions caters for the coincident probability of a trip of a network element at times of peak demand (usually a 50% POE load forecast).


As described in our previous newsletters, asset ratings are generally derived using a set of deterministic parameters which provide a conservative calculation. The common approach is to assume that a network element has already tripped and compare the magnitude of forecast demand with the documented asset rating under N-1 conditions. Due to the availability of most network assets, the likelihood of a forecast demand actually exceeding the asset rating is very low.



However, the network demand is usually correlated with temperature, which impacts on asset ratings through convective winds. Similarly, asset availability is also correlated with weather, which affects both loads and the network ratings.


For this reason, it is necessary to consider the coincident probability of a load exceeding the actual asset rating for a given asset availability. This coincident probability then needs to be compared with an accepted probability of exceedance; which is commonly defined at 1% by most regulatory authorities.


One solution is to apply a Monte-Carlo assessment which uses an annual distribution of loads, an annual distribution of ratings and monthly statistics for asset availabilities. A time-domain approach is usually employed due to the collinearity between these three distributions. The application of this approach will correctly show that the likelihood of exceeding the actual ratings is much lower.



The difference between the deterministic criteria and actual reliability performance can be used ...

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As noted in last month’s newsletter, electricity networks are generally planned to ensure that firm supply is available during periods of peak demand on the network. This relies on ensuring that load is supplied to an acceptable level of risk.


In Australia this risk is commonly quantified by allowing the ‘N-1’ loading to exceed the rating of some transmission lines for 1% of the year. (N-1 refers to the ability for a network to operate with one element out of service).


Since there is a probabilistic term in most reliability criteria, it is tempting to apply Monte-Carlo approaches. However, these are generally avoided due to the co-linearity between the asset rating and the supplied load. Instead, a time-domain approach should be employed which uses at least 12 months worth of historical load and weather data. The weather data can be used to define the asset rating over the same period of time.


Limited Historical Data


If there is only 12-24 months worth of weather data, it is common practice to simply project the metered loads against the load forecasts. In this case, 12 months worth of metering data should be scaled to match the forecast peak demand in a particular year.



With the aid of a load flow package, each of these forecast loading profiles can be compared with the asset ratings that were applied at the same time in the year. This analysis can be compared against the accepted reliability criterion to determine when augmentation is actually required.


Large Historical Records


Where there is more weather or real-time rating history, it is possible to apply more conventional load forecasting methodologies. The first step is to compare the ‘N-1’ loading on an asset with the rating of the asset over the last 12 months. This analysis will identify how often the rating has actually been exceeded over the previous year. This point can then be plotted along with the historical performance. Future compliance can then be forecast using conventional approaches.



For instance, let’s assume that the network ratings were allowed to be exceeded for 1% of the year. Even though the peak demand exceeded the asset rating, the previous diagram suggests that corrective action will not be required for at least ...

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