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 stochasticprogramming 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.
In this paper we present a modeling framework for analyzing natural gas markets, taking into account the specific technological issues of gas transportation. We model the optimal dispatch of supply and demand in natural gas networks, with different objective functions, i.e., maximization of flow, and different economic surpluses. The models take into account the physical structure of the transportation networks, and examine the implications it has for economic analysis. More specifically, pressure constraints create system effects, and thus, changes in one part of the system may require significant changes elsewhere. The proposed network flow model for natural gas takes into account pressure drops and system effects when representing network flows. Pressure drops and pipeline flows are modeled by the Weymouth equation. A linearization of the Weymouth equation makes economic analyses computationally feasible even for large networks. However, in this paper, the importance of combining economics with a model for pressure drops and system effects is illustrated by small numerical examples.
We consider an electricity market with two sequential market clearings, for instance representing a day-ahead and a real-time market. When the rst market is cleared, there is uncertainty with respect to generation and/or load, while this uncertainty is resolved when the second market is cleared. We compare the outcomes of a stochastic market clearing model, i.e. a market clearing model taking into account both markets and the uncertainty, to a myopic market model where the rst market is cleared based only on given bids, and not taking into account neither the uncertainty nor the bids in the second market. While the stochastic market clearing gives a solution with a higher total social welfare, it poses several challenges for market design. The stochastic dispatch may lead to a dispatch where the prices deviate from the bid curves in the rst market. This can lead to incentives for selfscheduling, require producers to produce above marginal cost and consumers to pay above their marginal value in the rst market. Our analysis show that the wind producer has an incentive to deviate from the system optimal plan in both the myopic and stochastic model, and this incentive is particularly strong under the myopic model. We also discuss how the total social welfare of the market outcome under stochastic market clearing depends on the quality of the information that the system operator will base the market clearing on. In particular, we show that the wind producer has an incentive to misreport the probability distribution for wind.
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