10,244 research outputs found
Computational optimization of gas compressor stations: MINLP models versus continuous reformulations
When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to nonconvex mixed-integer nonlinear optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several continuous reformulations of the problem. The applicability and relevance of different model formulations, especially of those without discrete variables, is demonstrated by a computational study on both academic examples and real-world instances. In addition, we provide preliminary computational results for an entire network.German Federal Ministry of Economics and Technolog
Coupling conditions for isothermal gas flow and applications to valves
We consider an isothermal gas flowing through a straight pipe and study the
effects of a two-way electronic valve on the flow. The valve is either open or
closed according to the pressure gradient and is assumed to act without any
time or reaction delay. We first give a notion of coupling solution for the
corresponding Riemann problem; then, we highlight and investigate several
important properties for the solver, such as coherence, consistence, continuity
on initial data and invariant domains. In particular, the notion of coherence
introduced here is new and related to commuting behaviors of valves. We provide
explicit conditions on the initial data in order that each of these properties
is satisfied. The modeling we propose can be easily extended to a very wide
class of valves
Error analysis and model adaptivity for flows in gas networks
In the simulation and optimization of natural gas flow in a pipeline network, a hierarchy of models is used that employs different formulations of the Euler equations. While the optimization is performed on piecewise linear models, the flow simulation is based on the one to three dimensional Euler equations including the temperature distributions. To decide which model class in the hierarchy is adequate to achieve a desired accuracy, this paper presents an error and perturbation analysis for a two level model hierarchy including the isothermal Euler equations in semilinear form and the stationary Euler equations in purely algebraic form. The focus of the work is on the effect of data uncertainty, discretization, and rounding errors in the numerical simulation of these models and their interaction. Two simple discretization schemes for the semilinear model are compared with respect to their conditioning and temporal stepsizes are determined for which a well-conditioned problem is obtained. The results are based on new componentwise relative condition numbers for the solution of nonlinear systems of equations. More- over, the model error between the semilinear and the algebraic model is computed, the maximum pipeline length is determined for which the algebraic model can be used safely, and a condition is derived for which the isothermal model is adequate.DFG, TRR 154, Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerke
Design and operations of gas transmission networks
Problems dealing with the design and the operations of gas transmission networks are challenging. The difficulty mainly arises from the simultaneous modeling of gas transmission laws and of the investment costs. The combination of the two yields a non- linear non-convex optimization problem. To obviate this shortcoming, we propose a new formulation as a multi-objective problem, with two objectives. The first one is the investment cost function or a suitable approximation of it; the second is the cost of energy that is required to transmit the gas. This energy cost is approximated by the total energy dissipated into the network. This bi-criterion problem turns out to be convex and easily solvable by convex optimization solvers. Our continuous optimization formulation can be used as an efficient continuous relaxation for problems with non-divisible restrictions such as a limited number of available commercial pipe dimensions.gas transmission networks, reinforcement, convex optimization
An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers
In energy systems with high shares of weather-driven renewable power sources,
gas-fired power plants can serve as a back-up technology to ensure security of
supply and provide short-term flexibility. Therefore, a tighter coordination
between electricity and natural gas networks is foreseen. In this work, we
examine different levels of coordination in terms of system integration and
time coupling of trading floors. We propose an integrated operational model for
electricity and natural gas systems under uncertain power supply by applying
two-stage stochastic programming. This formulation co-optimizes day-ahead and
real-time dispatch of both energy systems and aims at minimizing the total
expected cost. Additionally, two deterministic models, one of an integrated
energy system and one that treats the two systems independently, are presented.
We utilize a formulation that considers the linepack of the natural gas system,
while it results in a tractable mixed-integer linear programming (MILP) model.
Our analysis demonstrates the effectiveness of the proposed model in
accommodating high shares of renewables and the importance of proper natural
gas system modeling in short-term operations to reveal valuable flexibility of
the natural gas system. Moreover, we identify the coordination parameters
between the two markets and show their impact on the system's operation and
dispatch
An exact solution method for binary equilibrium problems with compensation and the power market uplift problem
We propose a novel method to find Nash equilibria in games with binary
decision variables by including compensation payments and
incentive-compatibility constraints from non-cooperative game theory directly
into an optimization framework in lieu of using first order conditions of a
linearization, or relaxation of integrality conditions. The reformulation
offers a new approach to obtain and interpret dual variables to binary
constraints using the benefit or loss from deviation rather than marginal
relaxations. The method endogenizes the trade-off between overall (societal)
efficiency and compensation payments necessary to align incentives of
individual players. We provide existence results and conditions under which
this problem can be solved as a mixed-binary linear program.
We apply the solution approach to a stylized nodal power-market equilibrium
problem with binary on-off decisions. This illustrative example shows that our
approach yields an exact solution to the binary Nash game with compensation. We
compare different implementations of actual market rules within our model, in
particular constraints ensuring non-negative profits (no-loss rule) and
restrictions on the compensation payments to non-dispatched generators. We
discuss the resulting equilibria in terms of overall welfare, efficiency, and
allocational equity
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