To guarantee security of supply, network operators need to stress-test their infrastructure based on scenarios. It is not enough to use only historical data for these scenarios, because then we can only test for what we have already seen in the past. We also want to find especially challenging situations based directly on the capacity of the network. In this blog, we show how this is done with the help of a simple proxy measure. We use gas pipeline transmission as our example, but the idea also applies to other utility or transportation networks.
Network operations planning
In gas pipeline transmission many situations are possible, due to independent capacity contracts with entries and exits. As part of the liberalisation of the market, the transmission and sales of gas have become separate businesses. Each seller (and buyer) is now a customer of the network operator, while the operator is only responsible for transportation. As part of their agreement, the seller gets the right to inject gas up to a bound at a certain entry location. Within these bounds, sellers and buyers can then nominate the actual amounts on short notice.
Network operators need to guarantee security of supply. This involves making sure that the network infrastructure has sufficient capacity and flexibility to deal with many potential future scenarios. A scenario in this case is defined by source locations where the goods enter the network, and sink locations where they leave it, together with values on the volume of goods supplied or demanded at each location.
Stress tests for the network infrastructure can be performed virtually, with the help of simulation or optimisation tools. Expert planners can imagine a likely future scenario, plan how they would run the network in that case, and then simulate the physical flows to verify that the network stays within the operational boundaries. With optimisation models, the decisions on how to control the network can even be automated, allowing the planners to consider a larger number of scenarios.
The selection of scenarios for stress tests determines how confident we can be with the results. In principle, if we find just one plausible scenario where we fail to operate the network in a feasible way, we have proven that the technical capacity is insufficient for the set of currently valid contracts. Even if all evaluated scenarios can be managed, we need to make sure that these represent the actual possibilities well.
Scenarios based on historical data
Historical data can be used to find likely scenarios. We can analyse the past behaviour of demand and supply volumes, depending on seasonality and weather, and then generate new scenarios by random sampling. This allows us to recreate typical behaviour, focus on common cases, and even quantify how well we have covered the known range of values.
A data-driven approach might miss trends and exceptional situations. These limitations of the use of historical data could be met by manual modification of sampled scenarios, but even this approach is difficult to scale because there are so many ways to deviate from known behaviour. This is why we want to go beyond data analysis to directly find challenging scenarios based on a model that explicitly considers technical and contractual boundaries.
Transport momentum as proxy measure
Transportation situations are stressful if large volumes need to be transported over long distances. In gas pipelines, the physical flow is driven from high pressure at the entry points, while friction leads to pressure losses. Therefore, pressure needs to be propped up at compressor stations placed along the pipelines. These compressors have limited capacity and their operation leads to costs based on their fuel consumption, which increases with volume.
A simple proxy measure allows us to quantify the difficulty of scenarios. Instead of modelling the physical aspects of the gas directly, in terms of pressure and flow rates, we approximate the pressure loss with the so-called transport momentum. This is defined as the product of the transported amount with the distance, i.e., the length of the pipe. The best operation of a network, in terms of throughput capacity and cost, is one that routes the flow in a way that minimizes the total transport momentum. By comparing the transport momentum resulting in different scenarios, we can rank these in terms of difficulty.
The situation on the left leads to a large transport momentum, because we must cover the long distance from the north to the south for a total volume of 5 units. In the situation on the right, a larger volume of 10 units is transported, but it is still easier because we can match nearby entries with exits.
Worst case scenarios from optimization models
We can find the situation where transport momentum is maximised, despite the best efforts of the operator. Given the data on the transportation network with distance information as well as a fixed scenario specifying supply and demand, we can formulate an optimisation model that will find the routing of flow leading to the minimal transport momentum. But we can even go beyond that and introduce another level of decisions where the model now decides on the supply and demand values that make sure the transport momentum results in as high a value as possible, even when using the best routing. For details on this so-called bilevel optimisation approach, see the description in the technical report [1].
Are you confident that the scenarios used in your analysis sufficiently cover possibilities that the future may bring? Would the transport momentum provide a good approximation in your specific situation? We invite you to reach out and discuss how we can help you remain confident in your stress testing.
Robert Schwarz
info@doingthemath.nl