544 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 1, JANUARY 2015 Look Ahead Robust Scheduling of Wind-Thermal System With Considering Natural Gas Congestion Cong Liu, Member, IEEE, Changhyeok Lee, and Mohammad Shahidehpour, Fellow, IEEE Abstract—Natural gas pipeline congestion will impact on the fuel adequacy of several natural gas fired generating units at the same time. This letter focuses on the development of a robust optimiza- tion methodology for the scheduling of quick start units when con- sidering natural gas resource availability constraints. Natural gas transmission will be approximated by linear constraints, and the linepack capacity of pipelines will be considered in the proposed model. Case studies show the effectiveness of the proposed model and algorithms. Index Terms—Natural gas electric coordination, renewable en- ergy, robust optimization, unit commitment. I. INTRODUCTION N ATURAL gas fired generating units play an important role in an electric power system. The quick start capabilities and fast ramping attribute of gas fired generating units like hydro units are cru- cial to compensate renewable generation forecast errors, contingen- cies, and load variations. Natural gas fuel availability will affect power system operation and security. If natural gas pipeline congestion oc- curs, the gas operator is likely to limit the amount of the natural gas delivered to gas-fired generating plants because most of them hold in- terruptible transportation contracts [1], [2]. In addition, renewable en- ergy uncertainty will result in uncertain natural gas usage of gas-fired generating units [3]. Therefore, in operating day closed to the real time, it is necessary to include natural gas constraints and renewable uncer- tainty into the look-ahead scheduling problem. Robust optimization models the uncertainty using a deterministic set (e.g., set of possible scenarios or range of possible values for the un- certain parameters) without any probabilistic description. It provides a robust solution that is immune to any possible scenario of the un- certainty set, which is an important aspect in the security constrained scheduling of electric power systems. The robust optimization often solves the so-called mini-max bilevel problem, which finds the solu- tion minimizing worst-case cost or infeasibility that is maximized over the uncertainty set. In [2]–[4], different models are proposed to deal with the combined optimization of electricity and natural gas scheduling problem. In this letter, the proposed model is for the look-ahead robust scheduling of gas-fired units in a utility or independent system operator (ISO) in the Manuscript received September 27, 2013; revised March 24, 2014; accepted May 05, 2014. Date of publication June 06, 2014; date of current version De- cember 18, 2014. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Ar- gonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. This work was supported by the U.S. Department of Energy, Office of Electricity Delivery and Energy. Paper no. PESL-00135-2013. C. Liu is with Argonne National Laboratory, Decision and Information Sci- ence, Argonne, IL 60439 USA. C. Lee is with Northwestern University, Evanston, IL 60208 USA. M. Shahidehpour is with the Illinois Institute of Technology, Chicago, IL 60616 USA. Digital Object Identifier 10.1109/TPWRS.2014.2326981 Fig. 1. Constant traveling time of natural gas flow. U.S. that has a large number of gas-fired quick-start generating units. We integrate the linearly approximated natural gas flow constraints into the proposed robust optimization tool. This model can lead to more secured commitments of quick-start gas-fired units under load variation and potential renewable ramping events. II. MODELING OF NATURAL GAS TRANSMISSION SYSTEM The transient natural gas flow can be represented as partial differen- tial equations (PDEs) for time and position which are dependent natural gas density, mass flow, flow velocity, and pressure [2]. Although the PDEs can be transformed into nonlinear algebraic difference equations [3], [4], the optimization with those constraints is still nonconvex. It has been found to be reasonable to use a linear DC power-flow model in power markets, and this allowed us to clear the markets on given time- frame or interpret the results. Similarly, reasonable assumptions can be made to establish a linear approximation for the natural gas flow. Developing a linear model depends on appropriate tradeoffs and approximation. For example, one simplifying assumption would be isothermic conditions. In addition, because gas pipeline flow is turbu- lent, we may assume that natural gas horizontal axial velocity is con- stant [6], [7]. With these two assumptions, the natural gas flow model can be approximated using a linear model. A natural gas pipeline is shown in Fig. 1. Equation (1) represents mass balance at gas node . is linepack capability representing natural gas amount stored in pipeline at time period . repre- sents the gas inflow of gas node through pipeline . If the practical gas mass flow of a pipeline is from to , is positive, other- wise, it is negative. can represents natural gas load of power generation, industry, company and residence. The sum of inflow minus the usage of natural gas equals to the total change of linepack capacity. Equation (2) denotes gas mass flow in given traveling speeds through a pipeline as shown in Fig. 1. Formulation (3) represents the upper bound and the lower bound of the line packing of a pipeline: (1) (2) (3) Natural gas used for power generation is represented as loads in (1). We can integrate the linear constraints (1)–(3) into the robust optimization framework presented in the next section. 0885-8950 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.