Marte Fodstad

Optimization Models for the Natural Gas Value Chain

In this paper we give an introduction to modelling the natural gas value chain including production, transportation, processing, contracts, and markets. The presentation gives insight in the complexity of planning in the natural gas supply chain and how optimization can help decision makers in a natural gas company coordinate the different activities. We present an integrated view from the perspective of an upstream company. The paper starts with decribing how to model natural gas transportation and storage, and at the end we present a stochastic portfolio optimization model for the natural gas value chain in a liberalized market.

Optimizing the Norwegian Natural Gas Production and Transport

The network for transport of natural gas on the Norwegian Continental Shelf, with 7,800 km of subsea pipelines, is the worlds largest offshore pipeline network. The gas flowing through this network represents approximately 15 percent of European consumption, and the system has a capacity of 120 billion standard cubic meters (bcm) a year. In a network of interconnected pipelines, system effects are prevalent, and the network must be analyzed as a whole to determine the optimal operation. SINTEF has developed a decision support tool, GassOpt, which is based on a mixed-integer program, to optimize the network configuration and routing for the main Norwegian shipper of natural gas, StatoilHydro, and the independent network operator, Gassco. GassOpt allows users to graphically model their network and run optimizations to find the best solutions quickly. StatoilHydro and Gassco use it to evaluate the current network and possible network extensions. Both companies use operations research (OR) methods in the departments that are responsible for transport planning and security of supply. Several new OR projects have grown out from this cooperation. StatoilHydro estimates that its accumulated savings related to the use of GassOpt were approximately US

Multi-horizon stochastic programming

2 billion in the period 1995--2008.

Optimal Medium-Term Hydropower Scheduling Considering Energy and Reserve Capacity Markets

Infrastructure-planning models are challenging because of their combination of different time scales: while planning and building the infrastructure involves strategic decisions with time horizons of many years, one needs an operational time scale to get a proper picture of the infrastructure’s performance and profitability. In addition, both the strategic and operational levels are typically subject to significant uncertainty, which has to be taken into account. This combination of uncertainties on two different time scales creates problems for the traditional multistage stochastic-programming formulation of the problem due to the exponential growth in model size. In this paper, we present an alternative formulation of the problem that combines the two time scales, using what we call a multi-horizon approach, and illustrate it on a stylized optimization model. We show that the new approach drastically reduces the model size compared to the traditional formulation and present two real-life applications from energy planning.

Hydropower scheduling in day-ahead and balancing markets

This paper describes a method for optimal scheduling of hydropower systems for a profit maximizing, price-taking, and risk neutral producer selling energy, and capacity to separate and sequentially cleared markets. The method is based on a combination of stochastic dynamic programming (SDP) and stochastic dual dynamic programming (SDDP), and treats inflow to reservoirs and prices for energy and capacity as stochastic variables. The proposed method is applied in a case study for a Norwegian watercourse, quantifying the expected changes in schedules, and water values when going from an energy-only market to a joint treatment of energy and reserve capacity markets.

Adding flexibility in a natural gas transportation network using interruptible transportation services

We present a stochastic mixed-integer model for the optimization of joint trade in the day-ahead and balancing markets. The model takes the perspective of a risk-neutral price-taking hydropower producer for a one-day planning horizon. The model is used to study the value of trading in both markets as opposed to day-ahead trades only. In particular we study how this value is affected by the flexibility in the production system. The results indicates a small added value from balancing market participation which is increasing as the production flexibility increases.

Co-optimizing sales of energy and capacity in a hydropower scheduling model

We present a modeling framework for analyzing if the use of interruptible transportation services can improve capacity utilization in a natural gas transportation network. The network consists of two decision makers: the transmission system operator (TSO) and a shipper of natural gas. The TSO is responsible for the routing of gas in the network and allocates capacity to the shipper to ensure that the security of supply in the network is within given bounds. The TSO can offer two different types of transportation services: firm and interruptible. Only firm services have a security of supply measure, while the interruptible services can freely be interrupted whenever the available capacity in the transportation network is not sufficiently large. We apply our modeling framework on a case study with realistic data from the Norwegian Continental Shelf. The results indicate substantial increased throughput and profits with the introduction of interruptible services.

A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints

This paper describes a model for optimal scheduling of hydroelectric systems for a price-taking producer selling energy and capacity to separate markets. The model is based on a combination of stochastic dynamic programming (SDP) and stochastic dual dynamic programming (SDDP), and treats inflow to reservoirs and energy prices as stochastic variables. It allows sales of capacity at a deterministic sequence of capacity reserve prices. Thus, the sales of energy and capacity is co-optimized within the SDDP framework. The presented model is tested on a Norwegian watercourse where the producer sells energy to the day-ahead market and capacity to the primary reserve markets. When adding the possibility to sell capacity in the model, the results show that less water is used during winter and more during summer/autumn in order to sell capacity.

Value of multi-market trading for a hydropower producer

We present a branch-and-bound algorithm for discretely-constrained mathematical programs with equilibrium constraints (DC-MPEC). This is a class of bilevel programs with an integer program in the upper-level and a complementarity problem in the lower-level. The algorithm builds on the work by Gabriel et al. (Journal of the Operational Research Society 61(9):1404–1419, 2010) and uses Benders decomposition to form a master problem and a subproblem. The new dynamic partition scheme that we present ensures that the algorithm converges to the global optimum. Partitioning is done to overcome the non-convexity of the Benders subproblem. In addition Lagrangean relaxation provides bounds that enable fathoming in the branching tree and warm-starting the Benders algorithm. Numerical tests show significantly reduced solution times compared to the original algorithm. When the lower level problem is stochastic our algorithm can easily be further decomposed using scenario decomposition. This is demonstrated on a realistic case.

Modeling start/stop in short-term multi-market hydropower scheduling

We present a case study for a price-taking hydropower producer trading in the three short-term energy markets, day-ahead, intra-day and the balancing market. The study uses a scheduling software with a detailed representation of a real Norwegian power plant optimizing the operations and trade for historical market data from 2015. The motivation for the study is to make an assessment of the value of trading in multiple markets relative to day-ahead trading only, utilizing a simplifying perfect foresight assumption. This gives the basis for assessing the value of developing more complex models with a more precise representation of uncertainty in the decision process. The analysis show a significant added value from participating in more markets than day-ahead, with the balancing market giving the largest contribution.