A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York

A series multi-step approach for operation Co-optimization of integrated power and natural gas systems

Power to gas units and gas turbines have provided considerable opportunities for bidirectional interdependency between electric power and natural gas infrastructures. This paper proposes a series of multi-step strategy with surrogate Lagrange relaxation for operation co-optimization of an integrated power and natural gas system. At first, the value of coordination capacity is considered as a contract to avoid dysfunction in each system. Then, the uncertainties and risks analysis associated with wind speed, solar radiation, and load fluctuation are implemented by generating stochastic scenarios. Finally, before employing surrogate Lagrange relaxation, the non-linear and non-convex gas flow constraint is linearized by two-dimension piecewise linearization. In the proposed procedure, constraints for energy storages and renewable energy sources are included. Two case studies are employed to verify the effectiveness of the proposed method. The surrogate Lagrange relaxation approach with coordination branch &amp; cut method enhances the accuracy of convergence and can effectively reduce the decision-making time.</p

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

Hybrid stochastic/robust flexible and reliable scheduling of secure networked microgrids with electric springs and electric vehicles

Electric spring (ES) as a novel concept in power electronics has been developed for the purpose of dealing with demand-side management. In this paper, to conquer the challenges imposed by intermittent nature of renewable energy sources (RESs) and other uncertainties for constructing a secure modern microgrid (MG), the hybrid distributed operation of ESs and electric vehicles (EVs) parking lot is suggested. The proposed approach is implemented in the context of a hybrid stochastic/robust optimization (HSRO) problem, where the stochastic programming based on unscented transformation (UT) method models the uncertainties associated with load, energy price, RESs, and availability of MG equipment. Also, the bounded uncertainty-based robust optimization (BURO) is employed to model the uncertain parameters of EVs parking lot to achieve the robust potentials of EVs in improving MG indices. In the subsequent stage, the proposed non-linear problem model is converted to linear approximated counterpart to obtain an optimal solution with low calculation time and error. Finally, the proposed power management strategy is analyzed on 32-bus test MG to investigate the hybrid cooperation of ESs and EVs parking lot capabilities in different cases. The numerical results corroborate the efficiency and feasibility of the proposed solution in modifying MG indices.© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).fi=vertaisarvioitu|en=peerReviewed

A Conic Model for Electrolyzer Scheduling

The hydrogen production curve of the electrolyzer describes the non-linear and non-convex relationship between its power consumption and hydrogen production. An accurate representation of this curve is essential for the optimal scheduling of the electrolyzer. The current state-of-the-art approach is based on piece-wise linear approximation, which requires binary variables and does not scale well for large-scale problems. To overcome this barrier, we propose two models, both built upon convex relaxations of the hydrogen production curve. The first one is a linear relaxation of the piece-wise linear approximation, while the second one is a conic relaxation of a quadratic approximation. Both relaxations are exact under prevalent operating conditions. We prove this mathematically for the conic relaxation. Using a realistic case study, we show that the conic model, in comparison to the other models, provides a satisfactory trade-off between computational complexity and solution accuracy for large-scale problems

Pressure Fluctuations in Natural Gas Networks caused by Gas-Electric Coupling

The development of hydraulic fracturing technology has dramatically increased the supply and lowered the cost of natural gas in the United States, driving an expansion of natural gas-fired generation capacity in several electrical inter-connections. Gas-fired generators have the capability to ramp quickly and are often utilized by grid operators to balance intermittency caused by wind generation. The time-varying output of these generators results in time-varying natural gas consumption rates that impact the pressure and line-pack of the gas network. As gas system operators assume nearly constant gas consumption when estimating pipeline transfer capacity and for planning operations, such fluctuations are a source of risk to their system. Here, we develop a new method to assess this risk. We consider a model of gas networks with consumption modeled through two components: forecasted consumption and small spatio-temporarily varying consumption due to the gas-fired generators being used to balance wind. While the forecasted consumption is globally balanced over longer time scales, the fluctuating consumption causes pressure fluctuations in the gas system to grow diffusively in time with a diffusion rate sensitive to the steady but spatially-inhomogeneous forecasted distribution of mass flow. To motivate our approach, we analyze the effect of fluctuating gas consumption on a model of the Transco gas pipeline that extends from the Gulf of Mexico to the Northeast of the United States.Comment: 10 pages, 7 figure