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

doi:10.1109/TSTE.2016.2615104

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

Journal Article•DOI•

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

Chuan He¹, Lei Wu², Tianqi Liu¹, Mohammad Shahidehpour³•Institutions (3)

Sichuan University¹, Clarkson University², Illinois Institute of Technology³

01 Apr 2017-IEEE Transactions on Sustainable Energy (IEEE)-Vol. 8, Iss: 2, pp 658-670

TL;DR: In this paper, a robust co-optimization scheduling model was proposed to study the coordinated optimal operation of the two energy systems, while considering power system key uncertainties and natural gas system dynamics.

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Abstract: 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.

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Journal Article•DOI•

Distributed Multi-Energy Operation of Coupled Electricity, Heating, and Natural Gas Networks

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Da Xu¹, Qiuwei Wu², Bin Zhou¹, Canbing Li¹, Li Bai³, Sheng Huang² - Show less +2 more•Institutions (3)

Hunan University¹, Technical University of Denmark², University of Pisa³

01 Oct 2020-IEEE Transactions on Sustainable Energy

TL;DR: A fully-distributed consensus-based alternating direction method of multipliers (ADMM) approach with only neighboring information exchange required is developed to optimize the multi-energy flows while considering the local energy-autonomy of heterogeneous energy hubs.

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Abstract: This article proposes a distributed multi-period multi-energy operational model for the multi-carrier energy system. In this model, energy hubs function as distributed decision-makers and feature the synergistic interactions of generation, delivery, and consumption of coupled electrical, heating, and natural gas energy networks. The multi-period multi-energy scheduling is a challenging optimization problem due to its strong couplings and inherent nonconvexities within the multi-energy networks. The original problem is thus reformulated as a mixed integer second-order cone programming (MISOCP) and subsequently solved with a sequential second-order cone programming (SOCP) approach to guarantee a satisfactory convergence performance. Furthermore, a fully-distributed consensus-based alternating direction method of multipliers (ADMM) approach with only neighboring information exchange required is developed to optimize the multi-energy flows while considering the local energy-autonomy of heterogeneous energy hubs. The proposed methodology is performed and benchmarked on a four-hub urban multi-energy system over a 24 hourly scheduling periods. Simulation results demonstrated the superiority of the proposed scheme in system operational economy and renewable energy utilization, and also verify the effectiveness of the proposed distributed approach.

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195 citations

Cites background or methods from "Robust Co-Optimization Scheduling o..."

...The integrated optimal energy flows of electricity-gas networks were studied in [6]–[8], and their combined economic dispatch under different spatio-temporal scales were investigated in [9]–[11]....
[...]
...in [8], [9], [24], CHP serves as the only coupling devices and its generation/demand information are exchanged between electricity and heating/gas network operators to achieve the consensus....
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...ADMM-based approaches in [9], [29]–[31] are fully distributed which can preserving the information privacy and decisionmaking independency of subsystems....
[...]
...Compared to these techniques, the alternating direction method of multipliers (ADMM) approach in [28] inherits and combines the decomposability of Lagrangian relaxation and convergence performance of the method of multipliers, which has been successfully applied in different scenarios [7]–[9], [29]–[31]....
[...]

Journal Article•DOI•

Robust Constrained Operation of Integrated Electricity-Natural Gas System Considering Distributed Natural Gas Storage

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Yubin He¹, Mohammad Shahidehpour², Zhiyi Li³, Chuangxin Guo¹, Bingquan Zhu - Show less +1 more•Institutions (3)

Zhejiang University¹, King Abdulaziz University², Illinois Institute of Technology³

01 Jul 2018-IEEE Transactions on Sustainable Energy

TL;DR: Simulations show that the proposed storage model is effective in the robust SCUC solution for IEGS considering possible N − k contingencies with limited natural gas adjustments, and distributed natural gas storage is included to smooth out power system demand curve.

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Abstract: A robust security-constrained unit commitment (robust SCUC) model is proposed in this paper to enhance the operational reliability of integrated electricity-natural gas system (IEGS) against possible transmission line outages. In this work, adjustable capability of natural gas contract is considered to avoid dramatic changes in real-time gas demand. Distributed natural gas storage is also included to smooth out power system demand curve and further improve operational efficiency at normal state and during contingencies. Nonlinear and nonconvex natural gas flow functions are relaxed into second-order cone (SOC) constraints, then the SOC-based column and constraint generation method is adopted to solve the proposed two-stage robust convex optimization problem. In this iterative method, the security-check subproblem feeds back worst case constraints to the first-stage master problem, until no violated scenarios can be detected. Simulations tested on 6-bus-6-node and 118-bus-10-node IEGS with natural gas storage show that the proposed storage model is effective in the robust SCUC solution for IEGS considering possible N − k contingencies with limited natural gas adjustments.

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179 citations

Cites methods from "Robust Co-Optimization Scheduling o..."

...Robust optimization for IEGS in distributed structures was studied based on ADMM in [20]....
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Journal Article•DOI•

Decentralized Energy Management for Networked Microgrids in Future Distribution Systems

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Hongjun Gao¹, Junyong Liu¹, Lingfeng Wang², Zhenbo Wei¹•Institutions (2)

Sichuan University¹, University of Wisconsin–Milwaukee²

01 Jul 2018-IEEE Transactions on Power Systems

TL;DR: A decentralized energy management framework to coordinate the power exchange between DS and MGs based on the alternating direction method of multipliers algorithm in a fully decentralized fashion is proposed.

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Abstract: An increasing amount of distributed energy resources is being integrated into both distribution systems (DSs) and networked microgrids (MGs). The coordination among DSs and MGs becomes essential for DS operators and MG operators considering the high uncertainties of renewable energies and load demands. In this paper, we propose a decentralized energy management framework to coordinate the power exchange between DS and MGs based on the alternating direction method of multipliers algorithm in a fully decentralized fashion. The energy management model in each entity (DSs or MGs) is formulated using two-stage robust optimization to address the uncertainties of renewables and load demands. The problem is treated as a second order cone programming one based on a relaxed distflow model. Moreover, the robust model is solved by column and constraint generation algorithm, where cutting planes are introduced to ensure the exactness of second-order cone relaxation. Numerical results on a modified IEEE 33-bus system with three MGs validate the effectiveness of the proposed method.

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156 citations

Cites background or methods from "Robust Co-Optimization Scheduling o..."

...Further, it is noteworthy that the improved tractable approach in [36] and [37] can also be introduced to deal with the integrality challenge if the model cannot converge within an acceptable number of iterations....
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...Certainly, some heuristic approaches such the alternating optimization procedure [36] and the relax-round-polish procedure [37] can be introduced to deal with the integrality challenge if the model cannot converge in an acceptable number of iterations....
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Proceedings Article•DOI•

A fast technique for unit commitment problem by extended priority list

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Tomonobu Senjyu¹, K. Shimabukuro¹, Katsumi Uezato¹, Toshihisa Funabashi²•Institutions (2)

University of the Ryukyus¹, Meidensha²

13 Jul 2003

TL;DR: This paper introduces a new unit commitment problem, adapting extended priority list (EPL) method, and proposes a method to modify unit schedule using problem specific heuristics to fulfill operational constraints.

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Abstract: This paper introduces a new unit commitment problem, adapting extended priority list (EPL) method. The EPL method consists of two steps, in the first step we get rapidly some initial unit commitment problem schedules by priority list (PL) method. At this step, operational constraints are disregarded. In the second step unit schedule is modified using the problem specific heuristics to fulfill operational constraints. To calculate efficiently, however, note that some heuristics is applied only to solutions can expect improvement. Several numerical examples demonstrate the effectiveness of proposed method.

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156 citations

Journal Article•DOI•

Decentralized Optimization of Multi-Area Electricity-Natural Gas Flows Based on Cone Reformulation

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Yubin He¹, Mingyu Yan², Mohammad Shahidehpour³, Zhiyi Li³, Chuangxin Guo¹, Lei Wu⁴, Yi Ding¹ - Show less +3 more•Institutions (4)

Zhejiang University¹, Huazhong University of Science and Technology², Illinois Institute of Technology³, Clarkson University⁴

01 Jul 2018-IEEE Transactions on Power Systems

TL;DR: The proposed approach demonstrates the merits of the decentralized operation and control of a multi-area integrated electricity-natural gas system (IEGS), in terms of large-scale modeling requirements, faster computations, and data management for local sensitivity analyses.

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Abstract: A large-scale integrated energy system can represent several subsystems representing areas that are tied by electricity and natural gas networks. Accordingly, we propose a decentralized optimal energy flow (DOEF) calculation as compared with a centralized solution method. The proposed approach demonstrates the merits of the decentralized operation and control of a multi-area integrated electricity-natural gas system (IEGS), in terms of large-scale modeling requirements, faster computations, and data management for local sensitivity analyses. Using the proposed decentralized structure, the communication burden is relatively light as individual area operators in a multi-area IEGS will make optimal dispatch decisions independently and the corresponding information is shared with adjacent subsystems. The reformulation of the second-order cone (SOC) is proposed using advanced sequential cone programming (SCP) to handle the nonlinear steady-state natural gas flow, which provides a feasible solution with a high degree of computational efficiency. Furthermore, an iterative alternating direction method of multipliers (I-ADMM) is adopted to manage the nonconvexity of integer variables, which guarantees a satisfactory convergence performance. Case studies on three multi-area IEGS validate the effectiveness of the proposed model in a multi-area IEGS.

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152 citations

Cites methods from "Robust Co-Optimization Scheduling o..."

...IEGS, only the scheduling of NGUs is selected as coupling variable [8], [12]....
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...Several decomposition methods are applied to an IEGS for achieving the synergistic operations of electric and natural gas networks [8], [12]....
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...To manage the uncertainty of wind-farm power outputs, operation characteristics of integrated system are studied in [7], [8]....
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...To expand its applications, an iterative ADMM (I-ADMM) is proposed in [16] by fixing integer variables, which is further modified and applied in the coordinated operation of electricitynatural gas systems [8]....
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...Compared to the ADMM algorithm given in [8], the integer feasible check is unnecessary in our methodology since the number of integer variables is reduced dramatically by applying the proposed SOC reformulation....
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References

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Open Access

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Book•

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

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Stephen Boyd¹, Neal Parikh¹, Eric Chu¹, Borja Peleato¹, Jonathan Eckstein² - Show less +1 more•Institutions (2)

Stanford University¹, Rutgers University²

23 May 2011

TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.

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Abstract: Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

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17,433 citations

"Robust Co-Optimization Scheduling o..." refers methods in this paper

...The proposed model is tackled via ADMM [17] by iteratively solving a power system subproblem and a gas system subproblem....
[...]
...In this section, the co-optimization model is decomposed into electricity and natural gas subproblems and first solved via standard ADMM [17]....
[...]
...The standard ADMM is used to solve the relaxed problem while guaranteeing the global convergence [17]....
[...]

Journal Article•DOI•

Renewable Power-to-Gas: A technological and economic review

[...]

M. Götz¹, J. Lefebvre¹, Friedemann Mörs¹, Amy McDaniel Koch¹, Frank Graf¹, Siegfried Bajohr¹, Rainer Reimert¹, Thomas Kolb¹ - Show less +4 more•Institutions (1)

Karlsruhe Institute of Technology¹

01 Jan 2016-Renewable Energy

TL;DR: In this paper, the authors compared the available electrolysis and methanation technologies with respect to the stringent requirements of the power-to-gas (PtG) chain such as low CAPEX, high efficiency, and high flexibility.

...read moreread less

1,841 citations

"Robust Co-Optimization Scheduling o..." refers background in this paper

...PtG is a promising technology that can contribute to tackling the issues of increased renewable generations [2], [3], [19]....
[...]
...In fact, there are several demonstration PtG project around the world [19], and it is expected to be widely deployed as the PtG technology is becoming more mature and economic....
[...]

Journal Article•DOI•

Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem

[...]

Dimitris Bertsimas¹, Eugene Litvinov², Xu Andy Sun³, Jinye Zhao², Tongxin Zheng² - Show less +1 more•Institutions (3)

Massachusetts Institute of Technology¹, ISO New England², Georgia Institute of Technology³

01 Feb 2013-IEEE Transactions on Power Systems

TL;DR: In this paper, a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty is proposed, which only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data.

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Abstract: Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.

...read moreread less

1,454 citations

"Robust Co-Optimization Scheduling o..." refers background or methods in this paper

...To verify the solution quality, [29] tested with different initial conditions and observed fast convergence and consistent results....
[...]
...The subproblem has a max-min form which is converted into a single-level bilinear optimization problem and solved via outer approximation (OA) method [20], [29]–[30]....
[...]

Journal Article•DOI•

Adjustable robust solutions of uncertain linear programs

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Aharon Ben-Tal, A. P. Goryashko, E. Guslitzer¹, Arkadi Nemirovski•Institutions (1)

Stanford University¹

01 Mar 2004-Mathematical Programming

TL;DR: The Affinely Adjustable Robust Counterpart (AARC) problem is shown to be, in certain important cases, equivalent to a tractable optimization problem, and in other cases, having a tight approximation which is tractable.

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Abstract: We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (‘‘non-adjustable variables’’), while the other part are variables that can be chosen after the realization (‘‘adjustable variables’’). We extend the Robust Optimization methodology ([1, 3-6, 9, 13, 14]) to this situation by introducing the Adjustable Robust Counterpart (ARC) associated with an LP of the above structure. Often the ARC is significantly less conservative than the usual Robust Counterpart (RC), however, in most cases the ARC is computationally intractable (NP-hard). This difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data. The ensuing Affinely Adjustable Robust Counterpart (AARC) problem is then shown to be, in certain important cases, equivalent to a tractable optimization problem (typically an LP or a Semidefinite problem), and in other cases, having a tight approximation which is tractable. The AARC approach is illustrated by applying it to a multi-stage inventory management problem.

...read moreread less

1,407 citations

"Robust Co-Optimization Scheduling o..." refers background in this paper

...1 Solution of Power System Subproblem: The power system subproblem minimizes (49) subject to (2)–(25), which is a two-stage adjustable robust optimization model [20] and [28]....
[...]

Journal Article•DOI•

Solving two-stage robust optimization problems using a column-and-constraint generation method

[...]

Bo Zeng¹, Long Zhao¹•Institutions (1)

University of South Florida¹

01 Sep 2013-Operations Research Letters

TL;DR: A computational study on a two-stage robust location-transportation problem shows that the column-and-constraint generation algorithm performs an order of magnitude faster than existing Benders-style cutting plane methods.

...read moreread less

1,010 citations

"Robust Co-Optimization Scheduling o..." refers methods in this paper

...The power system subproblem is solved by C&CG [18], and the nonlinear gas system subproblem is solved by converting into an MILP model....
[...]
...The C&CG is implemented via a master-subproblem framework....
[...]
...The power system subproblem is solved by C&CG, in which the identified worst case realizations are directly used in further iterations of ADMM to improve the computation speed....
[...]
...The power system subproblem is solved by C&CG in a master-subproblem framework....
[...]
...Solve power system subproblem: Solve (49) and (2)– (25) using the C&CG method in Section III-A.1, with given P̄ bit = P̂ g (r) it , P̄ b,ptg at = P̂ g ,ptg(r) at λp,it = λ (r) p,it , λp,at = λ (r) p,at , and the worst case natural gas usage cuts generated so far....
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