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Online probabilistic energy flow for hydrogen-power-heat system based on multi-parametric programming

APPLIED ENERGY 2024年 372卷

作者： Zhou, Yijia Peng, Hongyi Yan, Mingyu Huazhong Univ Sci & Technol State Key Lab Adv Electromagnet Technol Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan 430074 Peoples R China

The introduction of renewable energy introduces operational challenges for the modern multi-energy system. To accommodate the uncertainty, this paper proposes an online probabilistic energy flow for the hydrogen-powerheat system. First, a hydrogen-power-heat system model is established to depict the interdependency of multiple energy, in which hydrogen fuel cells interconnect hydrogen, power, and heat systems by converting the hydrogen into power and heat. The probabilistic energy flow is further built considering the uncertain wind power. An efficient algorithm based on multi-parametric programming (MPP) is proposed to enhance the computational performance of probabilistic multi-energy flow for online applications. The parameter region of the probabilistic multi-energy flow in MPP model is divided into multiple critical regions (CR). Each CR reveals a unique mapping relationship from uncertain wind power to system optimal solutions. Probabilistic energy flow could be quickly calculated based on mapping relationship rather than solving optimization problem. Therefore, the proposed method could be applied in online energy flow calculation. Numerical results tested on a 6-6-8 system and an improved 40-118 - 13 system validate the accuracy and efficiency of the proposed method in probabilistic energy flow calculation.

关键词： multi-parametric programming Hydrogen-power-heat system Probabilistic energy flow Critical region

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Explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

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COMPUTERS & CHEMICAL ENGINEERING 2024年 186卷

作者： Wang, Wenlong Wang, Yujia Tian, Yuhe Wu, Zhe Natl Univ Singapore Dept Chem & Biomol Engn Singapore 117585 Singapore West Virginia Univ Dept Chem & Biomed Engn Morgantown WV 26506 USA

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models. While ML models can capture nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. To address this issue, in this work, we propose an explicit ML-MPC framework for nonlinear processes using multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain a piecewise linear affine function that approximates the behaviors of ML models. Then, multi- parametric quadratic programming (mpQP) problems are formulated to generate the solution map for states in discretized state-space. Furthermore, to accelerate the implementation of explicit ML-MPC, a neighbor- first search algorithm is developed. Finally, an example of a chemical reactor is used to demonstrate the effectiveness of the explicit ML-MPC.

关键词： Machine learning Explicit model predictive control multi-parametric programming Nonlinear processes Chemical process control

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Improved Unit Commitment with Accurate Dynamic Scenarios Clustering Based on multi-parametric programming and Benders Decomposition

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Energy Engineering 2024年第6期121卷 1557-1576页

作者： Zhang Zhi Haiyu Huang Wei Xiong Yijia Zhou Mingyu Yan Shaolian Xia Baofeng Jiang Renbin Su Xichen Tian State Grid Corporation of China Beijing100031China Central China Branch State Grid Corporation of ChinaWuhan430077China School of Electric and Electronic Engineering Huazhong University of Science and TechnologyWuhan430074China China Electric Power Research Institute Co. Ltd.Beijing100192China

Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus *** results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.

关键词： Stochastic programming unit commitment scenarios clustering Benders decomposition multi-parametric programming

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A multi-parametric programming Based Analytic Method to Compute Consumer Offer Curve for Reserves

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Journal of Modern Power Systems and Clean Energy 2022年第2期10卷 542-546页

作者： Weiye Zheng David J.Hill Wenchuan Wu the School of Electrical Power Engineering South China University of TechnologyGuangzhouChina the Department of Electrical and Electronic Engineering The University of Hong KongHong KongChina the Department of Electrical Engineering Tsinghua UniversityBeijingChina

Abstract-An analytic method is proposed to compute the price-reserve offer curve at the consumer level in hierarchical direct load *** convexification of the consumer reserve provision is examined,and the analytic expression of the optimal solution within each critical region is ***,based on multi-parametric programming,a combinatorial enumeration method in conjunction with efficient reduction and pruning strategy is proposed to compute the optimal response of consumers in the whole price *** tests along with an application example in the bi-level aggregator pricing problem demonstrate the merit of this method.

关键词： Direct load control multi-parametric programming price-reserve offer curve analytic solution

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Dealing with infeasibility in multi-parametric programming for application to explicit model predictive control

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AUTOMATICA 2023年第1期157卷

作者： Falsone, Alessandro Bianchi, Federico Prandini, Maria Politecn Milan Dipartimento Elettron Informaz & Bioingn Via Ponzio 34-5 I-20133 Milan Italy Ric Sistema Energet RSE SpA Dept Generat Technol & Mat Via Rubattino 54 I-20134 Milan Italy

Motivated by explicit model predictive control, we address infeasibility in multi-parametric quadratic programming according to the exact penalty function approach, where some user-chosen parameter dependent constraints are relaxed and the 1-norm of their violation is penalized in the cost function. We characterize the relation between the resulting multi-parametric quadratic program and the original one and show that, as the penalty coefficient grows to infinity, the solution to the former provides a piecewise affine continuous function, which is an optimal solution for the latter over the feasibility region, while it minimizes the 1-norm of the relaxed constraints violation over the infeasibility region.& COPY;2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： multi-parametric programming Explicit model predictive control Exact penalty

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Adjustable robust optimization through multi-parametric programming

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OPTIMIZATION LETTERS 2020年第4期14卷 873-887页

作者： Avraamidou, Styliani Pistikopoulos, Efstratios N. Texas A&M Univ Texas A&M Energy Inst College Stn TX 77843 USA

Adjustable robust optimization (ARO) involves recourse decisions (i.e. reactive actions after the realization of the uncertainty, 'wait-and-see') as functions of the uncertainty, typically posed in a two-stage stochastic setting. Solving the general ARO problems is challenging, therefore ways to reduce the computational effort have been proposed, with the most popular being the affine decision rules, where 'wait-and-see' decisions are approximated as affine adjustments of the uncertainty. In this work we propose a novel method for the derivation of generalized affine decision rules for linear mixed-integer ARO problems through multi-parametric programming, that lead to the exact and global solution of the ARO problem. The problem is treated as a multi-level programming problem and it is then solved using a novel algorithm for the exact and global solution of multi-level mixed-integer linear programming problems. The main idea behind the proposed approach is to solve the lower optimization level of the ARO problem parametrically, by considering 'here-and-now' variables and uncertainties as parameters. This will result in a set of affine decision rules for the 'wait-and-see' variables as a function of 'here-and-now' variables and uncertainties for their entire feasible space. A set of illustrative numerical examples are provided to demonstrate the potential of the proposed novel approach.

关键词： Adjustable robust optimization multi-parametric programming Tri-level programming

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Integrating Heterogeneous Demand Response into N-1 Security Assessment by multi-parametric programming

Integrating Heterogeneous Demand Response into N-1 Security ...

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IEEE-Power-and-Energy-Society Innovative Smart Grid Technologies Conference (ISGT)

作者： Ruan, Guangchun Zhong, Haiwang Xia, Qing Kang, Chongqing Wang, Qiang Cao, Xin Tsinghua Univ Dept Elect Engn State Key Lab Beijing Peoples R China State Grid Hebei Elect Power CoLtd Wuhan Hubei Peoples R China

ISBN: (纸本)9781728131030

With the rapid growth of distributed energy resource integration, the power system is facing increased challenge of operation security. Demand response, as an underutilized resource, has shown great potential to support system security. This paper proposes a novel scheme to integrate heterogeneous demand side resources in the N-1 security assessment, which contains two steps: demand feature compression and joint scheduling with demand response. The general control model is formulated by multi-parametric programming to analyze various demand response resources and eliminate the privacy concerns. Cases studies validate the efficiency of proposed method, showing the underlying benefit of demand side participation.

关键词： demand response power system security assessment N-1 criteria multi-parametric programming

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Impact of Energy Storage Unit on Power System Economic Dispatch: A multi-parametric programming Method and its Implication on Energy Storage Sizing 39

Impact of Energy Storage Unit on Power System Economic Dispa...

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39th Chinese Control Conference (CCC)

作者： Fang, Baomin Wu, Danman Li, Yanhe Huang, Shaowei Mei, Shengwei State Grid Qinghai Elect Power Co Dispatch Control Ctr Xining Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

ISBN: (纸本)9789881563903

The energy storage unit (ESU) is helpful for shaving the peak and filling the valley demands, as well as compensating the volatility of renewable generation. The performance mainly depends on the maximum charging/discharging power (in MW) and energy capacity (in MWh). This paper proposes a multi-parametric linear programming model to investigate and describe the impact of MW/MWh parameters of the energy storage unit on the economic operation of bulk power systems in a geometric manner. By employing duality theory, the optimal value function of the economic dispatch problem is approximated via piecewise linear functions which are convenient for visualization. The optimal value function delivers useful information on energy storage sizing subject to a given budget, which is elaborated as an application of the proposed method. The effectiveness of the model and method is validated via a modified IEEE 39-bus system.

关键词： bulk power system economic dispatch energy storage unit multi-parametric programming

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Impact of Energy Storage Unit on Power System Economic Dispatch: A multi-parametric programming Method and its Implication on Energy Storage Sizing

Impact of Energy Storage Unit on Power System Economic Dispa...

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第三十九届中国控制会议

作者： Baomin Fang Danman Wu Yanhe Li Shaowei Huang Shengwei Mei Dispatch Control Center State Grid Qinghai Electric Power Company Department of Electrical Engineering Tsinghua University

The energy storage unit（ESU） is helpful for shaving the peak and filling the valley demands, as well as compensating the volatility of renewable generation. The performance mainly depends on the maximum charging/discharging power（in MW）and energy capacity（in MWh）. This paper proposes a multi-parametric linear programming model to investigate and describe the impact of MW/MWh parameters of the energy storage unit on the economic operation of bulk power systems in a geometric manner. By employing duality theory, the optimal value function of the economic dispatch problem is approximated via piecewise linear functions which are convenient for visualization. The optimal value function delivers useful information on energy storage sizing subject to a given budget, which is elaborated as an application of the proposed method. The effectiveness of the model and method is validated via a modified IEEE 39-bus system.

关键词： bulk power system economic dispatch energy storage unit multi-parametric programming

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Impact of Energy Storage on Economic Dispatch of Distribution Systems: A multi-parametric Linear programming Approach and Its Implications

IEEE OPEN ACCESS JOURNAL OF POWER AND ENERGY

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IEEE OPEN ACCESS JOURNAL OF POWER AND ENERGY 2020年第1期7卷 243-253页

作者： Wei, Wei Wu, Danman Wang, Zhaojian Mei, Shengwei Catalao, Joao P. S. Tsinghua Univ State Key Lab Power Syst Dept Elect Engn Beijing 100084 Peoples R China Univ Porto Fac Engn P-4200465 Porto Portugal INESC TEC P-4200465 Porto Portugal

As a main fiexible resource, energy storage helps smooth the volatility of renewable generation and reshape the load profile. This paper aims to characterize the impact of energy storage unit on the economic operation of distribution systems in a geometric manner that is convenient for visualization. Posed as a multi-parametric linear programming problem, the optimal operation cost is explicitly expressed as a convex piecewise linear function in the MW/MWh parameter of the energy storage unit. Based on duality theory, a dual linear programming based algorithm is proposed to calculate an approximate optimal value function (OVF) and critical regions, circumventing the difficulty of degeneracy, a common challenge in the existing multi-parametric linear programming solvers. When the uncertainty of renewable generation is considered, the expected OVF can be readily established based on OVFs in the individual scenarios, which is scalable in the number of scenarios. The OVF delivers abundant sensitivity information that is useful in energy storage sizing. Leveraging the OVFs, a robust stochastic optimization model is proposed to determine the optimal MW-MWh size of the storage unit subject to a given budget, which gives rise to a simple linear program. Case study provides a clear sketch of the outcome of the proposed method, and suggests that the optimal energy-power ratio of an energy storage unit is between 5 and 6 from the economical perspective.

关键词： Distribution system energy storage unit multi-parametric programming optimal value function approximation

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