AbstractâNatural gas pipeline congestion will impact on the fuel adequacy of several natural gas fired generating units at the same time. This letter focuses on ...
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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 optimization methodology for the scheduling of quick start units when considering 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 energy, robust optimization, unit commitment. I. INTRODUCTION
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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 crucial to compensate renewable generation forecast errors, contingencies, and load variations. Natural gas fuel availability will affect power system operation and security. If natural gas pipeline congestion occurs, the gas operator is likely to limit the amount of the natural gas delivered to gas-fired generating plants because most of them hold interruptible transportation contracts [1], [2]. In addition, renewable energy 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 uncertainty 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 uncertain parameters) without any probabilistic description. It provides a robust solution that is immune to any possible scenario of the uncertainty 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 solution 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 December 18, 2014. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, 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 Science, 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 differential 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 timeframe 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 turbulent, we may assume that natural gas horizontal axial velocity is constant [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 is linepack capability representing mass balance at gas node . reprenatural gas amount stored in pipeline at time period . sents the gas inflow of gas node through pipeline . If the practical is positive, othergas mass flow of a pipeline is from to , can represents natural gas load of power wise, it is negative. 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.
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LIU et al.: LOOK AHEAD ROBUST SCHEDULING OF WIND-THERMAL SYSTEM WITH CONSIDERING NATURAL GAS CONGESTION
III. ROBUST SCHEDULING MODEL
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TABLE I RESULTS FOR THE 118-BUS SYSTEM
(4) With the presence of uncertainty, the unit commitment decision needs to be made before the uncertainty revealed; however, the power generation can be determined after the uncertain parameters are observed as a recourse. Under robust feasibility criteria, this leads to the two-stage robust scheduling problem as shown in (4), where and are the uncertainty sets of load and wind, represents commitment decisions in the first corresponds to and , the forecasted load and wind. stage. The second stage problem is to check the feasibility of the constraint including natural gas transmission constraints for and . any given represents the second stage variables. The solution of the proposed model uses the column-and-constraint generation algorithm [5]. Master problem and subproblem are solved iteratively. The worst cases are selected through solving subproblem and are added into master problem as new constraints. The subproblem is max-min bilevel programming problem. After taking the dual of inner problem, the subproblem becomes a bilinear programming problem. We transform bilinear program into mixed integer linear program after introducing binary variables.
TABLE II COMPUTATIONAL PERFORMANCE OF ROBUST MODEL
In the second part, we consider multi-period robust scheduling problems and study their computational performance. In look-ahead scheduling problem, the time is closed to real-time operation. The time horizon in optimization problem is usually less than or equal to 4 periods. The wall clock time and the number of iteration for multi-period look-ahead scheduling problems are exhibited in Table II. When the number of time periods increases, the computational time also increases rapidly. However, the computational time is acceptable in the framework of a look-ahead scheduling problem. V. CONCLUSION
IV. CASE STUDIES We apply the model into the IEEE 118-bus system that include 3 areas, 54 generators, and 186 transmission lines. The penetration level of wind power generation is 20%. We assume the interval 20% of uncertainty set around the forecast values as follows: the wind power generation for the each one of three wind farms each 3% of the total load for each time period. A time period, and pipeline supply natural gas to 20 gas-fired generating units in area 2. We solve the problem to the optimality. In the first part, we consider one time period and compare the difference between results of deterministic unit commitment and robust unit commitment. The forecasted load for the next operation period is 3733 MW. Line pack capacity is crucial for the real-time operation of gas-fired generating units. Different initial line pack will be assumed in the case studies. Case 1) Deterministic scheduling with higher initial linepack Case 2) Deterministic scheduling with lower initial linepack Case 3) Robust scheduling with higher initial linepack Case 4) Robust scheduling with lower initial linepack With higher initial line pack in Case 1, 12 gas-fired generating units and 8 non-gas-fired generating units are committed to produce electricity. If the initial line pack is low in Case 2, only 10 gas-fired generating units are committed due to less amount of natural gas contained in the pipeline. However, the total number of committed units is 25 as shown in Table I. More gas fired and non-gas-fired generating units in Case 2 is committed compared to Case 1. In Case 3 and Case 4, two-stage robust scheduling methodology is employed to determine unit commitment. Robust methodology guarantees that any scenarios in the uncertainty set are feasible. Case 3 commits 13 gas generating units, which is one more than Case 1. Compared to Case 2, Case 4 commits two more non-gas generating units to cover the wind and load uncertainty as shown in Table I.
A robust optimization methodology-based look-ahead scheduling of quick-start generating units with natural gas transmission constraints is proposed. The method successfully guarantees that there are enough natural gas resources supplied to gas-fired generating units to balance the variation and intermittence of renewable energy, especially in the case when there is natural gas pipeline congestion. Linear approximation of natural gas flow model is proposed and used in the simulation. By using the proposed robust method, the operator does not need to sample scenarios during the simulation. Since the worst cases will be selected and checked during the process, the unit commitment of quick-start units are immunized to any scenarios in uncertainty set. Case studies based on the IEEE 118-bus system are given and illustrate the effectiveness and computational performance of the proposed method.
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