The significant growth in gas-fired units worldwide has increased the grade of interdependency between power and natural gas networks. Since these units are usually required to ramp up during the peak and backup intermittent renewable generation and contingencies, the power system tends to demand more flexibility and reliability from the gas system. This paper contributes with a novel mixed-integer linear programing (MILP) formulation that couples power and gas networks taking into account the gas traveling velocity and compressibility. As a result, the model accounts for the gas adequacy needed to assure the power system reliability in the short term. The robustness of the MILP formulation allows guaranteeing global optimality within predefined tolerances. Case studies integrate the IEEE 24-bus system and Belgian high-calorific gas network for validating the formulation.

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Integrated Power and Natural Gas Model for Energy Adequacy in Short-Term Operation

The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flow-pressure relations, material balances, and pressure bounds. The solution method is based on piecewise linear approximations of the nonlinear flow-pressure relations. The approximated problem is solved by an extension of the Simplex method. The solution method is tested on real-world data and compared with alternative solution methods.

The gas transmission problem solved by an extension of the simplex algorithm

The significant growth of gas-fired power plants and emerging power-to-gas (PtG) technology has intensified the interdependency between electricity and natural gas systems. This paper proposes a robust co-optimization scheduling model to study the coordinated optimal operation of the two energy systems. The proposed model minimizes the total costs of the two systems, while considering power system key uncertainties and natural gas system dynamics. Because of the limitation on exchanging private data and the challenge in managing complex models, the proposed co-optimization model is tackled via alternating direction method of multipliers (ADMM) by iteratively solving a power system subproblem and a gas system subproblem. The power system subproblem is solved by column-and-constraint generation (C&CG) and outer approximation (OA), and the nonlinear gas system subproblem is solved by converting into a mixed-integer linear programming model. To overcome nonconvexity of the original problem with binary variables, a tailored ADMM with a relax-round-polish process is developed to obtain high-quality solutions. Numerical case studies illustrate the effectiveness of the proposed model for optimally coordinating electricity and natural gas systems with uncertainties.

Robust Co-Optimization Scheduling of Electricity and Natural Gas Systems via ADMM

Interval optimization based operating strategy for gas-electricity integrated energy systems considering demand response and wind uncertainty

Continuous liberalization and interconnection of energy markets worldwide has raised concerns about the inherent interdependency between primary energy supply and electric systems. With the growing interaction among energy carriers, limitations on the fuel delivery are becoming increasingly relevant to the operation of power systems. This paper contributes with a novel formulation of a mixed-integer linear programing (MILP) security-constrained optimal power and gas flow. To this end, an iterative methodology, based on development of linear sensitivity factors, determines the stabilized post-contingency condition of the integrated network. The proposed model allows system operators not only to perform security analysis but also to adjust in advance state variables of the integrated system optimally and fast, so that $n-1$ contingencies do not result in violations. Case studies integrate the IEEE 24-bus system and a modified Belgian high-calorific gas network for analyzing the performance of the formulation and solution methodology.

Security-Constrained Optimal Power and Natural-Gas Flow

This paper proposes a methodology to identify and protect vulnerable components of connected gas and electric infrastructures from malicious attacks, and to guarantee a resilient operation by deploying valid corrective actions, while accounting for the interdependence of the gas pipeline network and power transmission network. The proposed mathematical formulation gives rise to to a trilevel optimization problem, where the lower level is a multiperiod economic dispatch of the gas–electric system and seeks operating strategies under available resources and given attack, the middle level distinguishes the most threatening attack on the coupled physical infrastructures, and the upper level provides optimal preventive decisions to reinforce the vulnerable components and increase the system resilience. By reformulating the lower level problem as a mixed integer linear programming, a nested column-and-constraint generation algorithm is developed to solve the min–max–min model. Case studies on two test systems demonstrate the effectiveness and efficiency of the proposed methodology.

Robust Defense Strategy for Gas–Electric Systems Against Malicious Attacks

Gas network optimization manages the gas transport by minimizing operating costs and fulfilling contracts between consumers and suppliers. This is an NPhard problem governed by non-convex and nonlinear gas transport functions that can be modeled by mixed integer linear programming (MILP) techniques. Under these methods, piecewise linear functions describe nonlinearities and binary variables avoid local optima due to non-convexities. This paper compares theoretically and computationally basic and advanced MILP formulations for the gas network optimization in dynamic or in steady-state conditions. Case studies are carried out to compare the performance of each MILP formulation for different network configurations, sizes and levels of complexity. In addition, since the accuracy of linear approximations significantly depends on the number and location of linear segments, this paper also proposes a goal programming method to construct a-priori the piecewise linear functions. This method is based on the minimization of the mean squared error of each approximation subject to predefined error goals.

http://www.optimization-online.org/DB_FILE/2014/10/4580.pdf

Gas Network Optimization: A comparison of Piecewise Linear Models

Private investors, flexibility, efficiency and environmental requirements from deregulated markets have led the existence and building of a significant number of combined-cycle gas turbines (CCGTs) in many power systems. These plants represent a complex optimization problem for the short-term planning unit commitment (UC) carried out by independent system operators due to their multiple operating configurations. Accordingly, this paper proposes a mixed-integer linear programming (MIP) formulation of the configuration-based model of CCGTs, which is commonly utilized for bid/offering market processes. This formulation is simultaneously tighter and more compact than analogous MIP-based models; hence, it presents a lower computational burden. The computational efficiency of the proposed formulation is demonstrated by solving network-constrained UC case studies, of different size and complexity, using three of the leading commercial MIP solvers: CPLEX, GUROBI, and XPRESS.

Carlos M. Correa-Posada

Papers

Integrated Power and Natural Gas Model for Energy Adequacy in Short-Term Operation

Security-Constrained Optimal Power and Natural-Gas Flow

Robust Defense Strategy for Gas–Electric Systems Against Malicious Attacks

Gas Network Optimization: A comparison of Piecewise Linear Models

Tight and Compact MIP Formulation of Configuration-Based Combined-Cycle Units