This winter, the electricity price in the south of Norway has reached levels over ten times higher than the price in the north. These differences are a result of capacity constraints and not surprisingly, Statnett is considering to increase the grid capacity. An obvious way would be to build new transmission lines, but this is very expensive and takes years to complete. The other option is to utilize the existing grid more efficiently.

What factors are limiting the transmission capacity? How do we estimate these limits, and can more data help us get closer to their *true *values? Together with some of my colleagues at the Data science team, I’ve been putting weather data to work in an attempt to calculate transmission capacities in a smarter way. Because** if we can safely increase the capacities of individual transmission lines, we might be able to increase the overall capacity between regions as well.**

## Too hot to handle

Transmission capacity is limited for a number reasons. If too much power flows through this *single transmission line* that connects a power producer and a consumer, there are at least three things that could go really wrong:

- The
**voltage**at the consumer could**drop**below acceptable levels - The
**conductor could suffer material damage**if the temperature goes beyond its thermal limit - The conductor could
**sag too close to the ground**as it expands with higher temperature

The sagging problem must be taken seriously to avoid safety hazard and wildfire risk, and regulations specify a minimum allowed clearance from the conductor to the ground.

Statnett calculates a *thermal rating* for each line in the transmission grid. These ratings restrict the power flow in the network in an attempt to always repect thermal limits and minimum clearance regulations. Today, these calculations rely on some consequential simplifications, and the resulting limits are generally considered to be on the conservative side.

Fresh weather data enables a different kind of calculation of these limits, and the ambition of our current work is to increase the current-carrying capacity, or *ampacity *of Norwegian transmission lines when it’s safe to do so. But before attempting to calculate better limits **indirectly**, using weather data, we first ran a project to estimate ampacity **directly**, using sensors.

## Estimating ampacity with sensors

A dynamic line rating (DLR) sensor is a piece of hardware that provides ampacity values based on *measurements*. **The sensor cannot measure the ampacity directly**, it is only able to make an estimate based on what it observes, which is typically the *sag *or *clearance to ground*.

We recently tested and evaluated DLR sensors from three different suppliers. **The results were mixed**, we experienced large ampacity deviations between the three.

DLR sensors come at a cost, and the reach of a sensor is limited to the single span where it is located. This is the motivation behind our **indirect** **approach **to calculate ampacity ratings, without using the DLR sensors.

## Calculating the ampacity

In our indirect model, we base our calculations on the method described in *CIGRE 601 Guide for thermal rating calculations of overhead lines *to calculate ampacity. In short, we need to solve a **steady-state heat balance equation** that accounts for *joule losses*, *solar heating*, *convective cooling* and *radiative cooling*:

**Joule losses heat the conductor** and increase as the current through the conductor increases. The losses are caused by the resistive and magnetic properties of the conductor.

**Solar radiation heats the conductor** and dependens on the solar position, which varies with the time of day and date of year. Cloud cover, the orientation of the line, the type of terrain on the ground and the properties of the conductor also influence the heating effect.

**Convection cools the conductor.** The effect is caused by the movement of the surrounding air and increases with the temperature difference between the conductor and the air. *Forced convection* on a conductor depends on the **wind speed** and the **wind direction** relative to the orientation of the span. A wind direction perpendicular to the conductor has the largest cooling effect. And even without wind, there will still be *natural convection*.

**Radiation cools the conductor.** The temperature difference between the conductor temperature and the **air temperature** causes a transmission of heat from the conductor to the surroundings and the sky.

**Convective cooling and joule heating have the most significant effect on the heat balance, **as the figure below shows. The solar heating and the radiative cooling are smaller in magnitude.

As it turns out, many of the parameters in the equation are weather-dependent. In the following sections I will explain three indirect models that go to different lengths of applying weather data when calculating thermal ratings.

## The simplest weather-based ampacity calculation: a static seasonal limit

Historically, a simple and common approach to the problem has been to establish **seasonal **ampacity ratings for a transmission line by considering the **worst-case seasonal weather conditions** of the **least advantageous span**. This approach can lead to limits such as:

- Summer:
**232 A** - Spring and autumn:
**913 A** - Winter:
**1913 A**

Such a model requires very little data, but has the disadvantage of being too conservative, providing a lower ampacity than necessary in all but the worst-case weather conditions. The *true *ampacities would vary over time.

## Including air temperature in the calculation

Statnett includes air temperatures in their ampacity calculations. The temperatures can come from measuring units or a forecast service. This approach is vastly more sophisticated than the static seasonal limits, but there are still many other factors where Statnett resorts to simplifying assumptions.

**The wind speed and wind direction are recognized as the most difficult to forecast.** The wind can vary a lot along the length of a span and over time. To overcome the modeling challenge, the traditional Statnett solution has been to assume constant wind speed from a fixed wind direction. The effect of solar heating is also reduced to a worst-case values for a set of different temperatures. **The end result is ampacity values that depend only on the air temperature**. The resulting ampacities are believed to be conservative, especially since the solar heating is often lower than the worst-case values.

However, **counterexamples **can be made, where the *true *ampacity would be *lower *than the values calculated by Statnett. Combinations of low wind speed, unfavourable wind direction and solar heating close to worst-case can happen in rare cases, especially for spans where winds are shielded by terrain. And of course, errors in the input air temperature data can also give a too high ampacity.

## Including more weather parameters

Our full weather-based model not only considers air temperature, but also **wind speed, wind direction, date and time **(to calculate solar radiation) **and the configuration of the transmission line span**.

Applying the wind speed and direction data is not straightforward. And at the same time, the consequences of incorrect ampacities are asymmetric. The additional capacity can never justify clearance violations or material damage of the conductor, so being right *on average* may not be a good strategy.

## Comparing the models

We compared the ampacity from DLR sensors to the three indirect, weather-based calculation approaches for a specific line in the summer, autumn and winter. The DLR sensor estimate should not be accepted as the *true ampacity*, but is considered to be the most accurate and relevant point of reference.

In summer, the static seasonal limit results in low utilization of the line and low risk, as expected. The current Statnett approach allows higher utilization, but without particularly high risk, since the limits are still conservative compared to the DLR sensor estimate. The weather-based approach overestimates the ampacity most of these four days in July, but drops below the DLR sensor estimate a few times.

Summer period.

Our autumn calculations tell a similar story. However, the difference between the current Statnett approach and the DLR sensors is even larger, indicating high potential for capacity increases with alternative methods.

Autumn period.

In winter, the static seasonal rating and the current Statnett approach are still more conservative that the DLR sensor, but the weather-based estimate is more conservative than the estimate of the DLR sensor in the chosen period.

Winter period.

The static seasonal limits and Statnett’s air temperature dependent limits are consistently more conservative than the approach with a DLR sensor. Our weather-based approach, on the other hand, give too optimistic ampacity ratings, with a few exceptions.

We think we have an idea why.

## Weather-based models require high quality weather data or forecasts

For all seasons, the weather-based approach stands out with its large ampacity variations. It is great that our model better reflects the weather-driven temperature dynamics, but the large variations also show the huge impact weather parameters (and their inaccuracies) have on the calculations.

The weather data we used to calculate ampacity were to a large extent *forecasts*, and even the best forecasts will be inaccurate. But even more imporantly: the weather data were never *calibrated to local conditions*. This will overestimate the cooling effect under some conditions. In reality, terrain and vegetation in the immediate surroundings of a power line can deflect much of the wind.

To calculate more accurate weather-based limits, we believe the weather parameters from a forecast **cannot be used directly without some form of adjustment**.

For the future, we would like to find a way to make these adjustments, such that we can increase the ampacity compared to Statnett’s current approach while reducing the risk of overestimation. Additionally, The Norwegian Meteorological Institute provides an *ensemble forecast* that gives additional information about the uncertainty of the weather forecast. In future work, we would like to use the uncertainty information in our indirect weather-based model.