Exploiting flexibility of combined-cycle gas turbines in power system unit commitment with natural gas transmission constraints and reserve scheduling

https://doi.org/10.1016/j.ijepes.2020.106460Get rights and content

Highlights

  • A power system unit commitment model with flexibility of CCGT is proposed.

  • Natural gas transmission constraints and reserve scheduling are considered.

  • The model is transformed into an iterative MISOCP problem.

  • Startup-shutdown cost and wind power curtailment can be reduced.

Abstract

With the integration of large-scale renewable energy including wind power into the power grid, efficient flexible resources are required for wind power accommodation. The combined-cycle gas turbines (CCGTs) are widely used in the power system with flexible operation characteristics, which leads to enhanced interdependencies between the power grid and the natural gas network. In this paper, a unit commitment (UC) model with natural gas transmission constraints and reserve scheduling considering the flexibility of CCGT with quick startup-shutdown and flexible operation characteristics is proposed, to reduce wind power curtailment and high startup and shutdown cost of conventional generation units in the power system. Considering the complex operating conditions of CCGT and the non-convexity of Weymouth equation in natural gas network, this paper adopts an improved mode-based model (MBM) for modeling of CCGT and converts the Weymouth equation into a second-order cone relaxation (SOCR) formulation with penalty term through a concave-convex process (CCP) to make the relaxation tight, thus transforming the UC model into an iterative mixed-integer second-order cone programming (MISOCP) problem to be efficiently solved. The effectiveness of the proposed model on reducing wind power curtailment and startup-shutdown cost is demonstrated through case studies.

Introduction

In recent years, energy and environmental crisis has become severe challenges. The large-scale integration of renewable energy into power grid has promoted the clean and low-carbon development of power system [1]. Power system with high proportion of renewable energy has become a worldwide trend. According to the Energy Research Institute of the National Development and Reform Commission of China, renewable energy can provide more than 60% of the energy supply by 2050, and installed wind power capacity will reach 2400 GW, accounting for 35.2% of the total power generation [2]. However, the randomness and fluctuation of wind power output bring new challenges to the flexible operation of power system [3].

The flexibility of power system refers to the capacity of the system to accept the uncertainties of load and renewable energy under the constraints of a certain time scale [4], [5]. Moreover, it is pointed out in [6] that the flexibility requirement mainly includes the reserve capacity and the ramping rate of generation units. Therefore, the fluctuation of load and wind power will lead to the increase of reserve requirement of the system [7], [8], [9], [10]. Besides, due to the long startup-shutdown time, high startup-shutdown cost and slow ramping rate of traditional coal-fired generation units (CFGU), it is difficult to meet the flexibility requirements of power system with high penetration of renewable energy. Compared with CFGU, combined-cycle gas turbines (CCGT) have advantages such as low startup-shutdown cost, fast startup-shutdown speed, ramping rate and flexible site selection, which can provide more sufficient flexibility requirements for power system [11].

However, the complex operating conditions of CCGT brings great challenge to the optimization operation of power system, for example, the unit commitment (UC) problem. By ignoring the different operation configurations of CCGT, CCGT is assumed to be a conventional generation unit in [12], which significantly improved the computational efficiency, but it is difficult to describe the real operating cost and physical characteristics of CCGT. In [13], the physical operation characteristics of each component in CCGT are accurately modeled, but due to the complexity of the model, this modeling method is more suitable for security analysis [14]. In [15], the mode transition space of each CCGT is defined and a mixed integer programming (MIP) model considering all feasible mode transitions is established. The works in [16], [17] focus on computational efficiency improvement by limiting the number of transitions allowed for each CCGT mode. A more compact MIP formula is proposed in [18] to improve the convergence and solving speed of MIP problems. However, the impact of CCGT flexibility on power system renewable energy accommodation, and the impact of natural gas system operation constraints should be considered.

With the increasing installed capacity of CCGT, the coupling between power grid and natural gas network is further deepened. The traditional independent analysis method for a single energy system is no longer applicable to the strongly coupled electric-gas integrated energy system. Many valuable works have been done in synergetic operation of power and natural gas systems [19], [20], [21], [22], [23], [24]. For the power system optimal operation model, the direct current optimal power flow (DCOPF) model is widely used [5], [16], [19], [25], which is easy to solve. For the natural gas system operation model, the steady-state operation model without considering the dynamic characteristics is widely used [22], [23], [24], [25]. However, the Weymouth equation of the natural gas network is a nonlinear non-convex equation, which brings great challenge to the solution of optimal operation models. In [24], [25], the optimal natural gas flow (OGF) model is constructed in mixed-integer linear programming (MILP) form by linearizing Weymouth equation to reduce the computational complexity. However, the efficiency and accuracy of the linearization method are difficult to be obtained simultaneously. The OGF model based on second-order cone relaxation (SOCR) is proposed in [26], which greatly improved the computational efficiency. However, this relaxation inevitably caused optimality gap due to the expansion of the feasible region.

In view of the above, this paper proposes a UC model for integrated power and natural gas systems with high proportion of wind power with natural gas transmission constraints and reserve scheduling considering the flexibility of CCGT with quick startup-shutdown and flexible operation characteristics. The major contributions of this paper are as follows:

  • 1)

    Based on the mode-based model (MBM) of CCGT, the mode transition matrix is introduced to establish a more concise and intuitive CCGT mode model, which can be effectively incorporated in the UC model.

  • 2)

    Based on the improved MBM of CCGT, a UC model of integrated power and natural gas systems with reserve scheduling is established and translated into an iterative MISOCP problem, and the impact of CCGT flexibility on power system with high penetration of wind power is analyzed for system operation economy improvement and wind power accommodation.

  • 3)

    Natural gas network operation constraints are taken into account and the non-convex Weymouth equation of natural gas system is transformed into a second-order cone (SOC) form with penalty term and a nonlinear concave-convex process (CCP) based algorithm is adopted to tighten converted SOC constraints.

The rest of this paper is organized as follows: Section Ⅱ introduces the operation characteristics of CCGT and establishes the MBM of CCGT. Section III presents the mathematical formulation of UC model with natural gas transmission constraints and reserve scheduling considering the flexibility of CCGT with quick startup-shutdown and flexible operation characteristics. In Section Ⅳ, the proposed UC model is translated into an iterative MISOCP problem. In Section Ⅴ, the numerical results on two testing systems are presented to demonstrate the effectiveness of the proposed model and the impacts of CCGT on wind power curtailment reduction. Section VI concludes the paper and present the future work.

Section snippets

Operating characteristics of CCGT

As a combined cycle turbine, CCGT is mainly composed of combustion power generation system (CPGS) and steam power generation system (SPGS). The CPGS includes combustion turbines (CTs) and combustion chambers (CCs), while the SPGS includes heat recovery steam generators (HRSGs) and steam turbines (STs). In the power generation process of CPGS, natural gas and compressed air are mixed and combust in CCs to generation the high temperature (above 1000℃) high-pressure gas, which is used to drive CTs

Problem formulation

The flexibility requirement in the power system mainly come from two aspects: i) daily load fluctuation and ii) daily fluctuation of renewable energy. With the increasing penetration of wind power and other renewable energy in the power system, the flexibility requirement of the system should be considered in the operation of power system. Therefore, in the proposed UC model, not only the reserve scheduling is considered, but also the natural gas network constraints are taken into account, so

Model transformation and solution method

The Weymouth equation (35) in natural gas network constraints is a nonlinear non-convex equation, which brings great challenge to the solution of the proposed UC model.

In fact, due to the slow gas dynamics operation characteristics of natural gas system, the daily flow direction is generally unchanged [12], [20], and the flow direction can be predicted in advance, thus the head node plf and the tail node plt of passive pipelines can be specified according to the flow direction:ypl,t2=Cpl2πplf,t2

Case study

In this section, we present numerical results on a modified IEEE 5-bus electricity network with a 7-node gas network and a modified IEEE 24-bus electricity network with a 14-node gas network to validate the effectiveness and performance of the proposed model and algorithm. The experiments are performed on a laptop with Intel(R) Core (TM) 2 Duo 2.6 GHz CPU and 4 GB memory. The proposed model is implemented on MATLAB with CVX [29] toolbox and solved by GUROBI 7.52 [30]. Refer to the penalty

Conclusion

In this paper, a UC model of power system with natural gas transmission constraints and reserve scheduling considering the flexibility of CCGT with quick startup-shutdown and flexible operation characteristics is proposed. Based on the proposed improved MBM of CCGT, the UC is modeled considering natural gas network constraints and reserve scheduling. The UC model is transformed into an iterative MISOCP formulation based on CCP to make the relaxation tight. The flexibility of CCGT with quick

CRediT authorship contribution statement

Tao Jiang: Conceptualization, Methodology. Chenguang Yuan: Data curation, Software. Rufeng Zhang: Software, Formal analysis. Linquan Bai: Software. Xue Li: Investigation, Software. Houhe Chen: Project administration. Guoqing Li: Supervision.

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgments

This work was supported in part by National Natural Science Foundation of China (Grant No. 51877033, 51677022), Jilin Province Key Research and Development Project (NO. 20200403066SF), International (Regional) Joint Research Project of National Natural Science Foundation of China (No. 52061635103).

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