Decomposition Of Large-scale Systems Research Articles

Optimization-based disjoint and overlapping epsilon decompositions of large-scale dynamical systems via graph theory

To address the complexity challenge of a large-scale system, the decomposition into smaller subsystems is very crucial and demanding for distributed estimation and control purposes. This paper proposes novel optimization-based approaches to decompose a large-scale system into subsystems that are either weakly coupled or weakly coupled with overlapping components. To achieve this goal, first, the epsilon decomposition of large-scale systems is examined. Then, optimization frameworks are presented for disjoint and overlapping decompositions utilizing bipartite graphs. Next, the proposed decomposition algorithms are represented for particular cases of large-scale systems using directed graphs. In contrast to the existing user-based techniques, the proposed optimization-based methods can reach the solution rapidly and systematically. At last, the capability and efficiency of the proposed algorithms are investigated by conducting simulations on three case studies, which include a practical distillation column, a modified benchmark model, and the IEEE 118-bus power system.

Optimization-based Disjoint and Overlapping Epsilon Decompositions of Large-scale Dynamical Systems via Graph Theory

To address the complexity challenge of a large-scale system, the decomposition into smaller subsystems is very crucial and demanding for distributed estimation and control purposes. This paper proposes novel optimization-based approaches to decompose a large-scale system into subsystems that are either weakly coupled or weakly coupled with overlapping components. To achieve this goal, first, the epsilon decomposition of large-scale systems is examined. Then, optimization frameworks are presented for disjoint and overlapping decompositions utilizing bipartite graphs. Next, the proposed decomposition algorithms are represented for particular cases of large-scale systems using directed graphs. In contrast to the existing user-based techniques, the proposed optimization-based methods can reach the solution rapidly and systematically. At last, the capability and efficiency of the proposed algorithms are investigated by conducting simulations on three case studies, which include a practical distillation column, a modified benchmark model, and the IEEE 118-bus power system.

The Optimal Operation of Parallel Pumping Stations for Inter-Basin Water Transfer Based on the Multi-Objective Optimization of a Single Pumping Station

A nonlinear mathematical model for the optimal operation of a parallel pumping station group was established with the objective of minimizing the operation costs of the station group considering the target quantity of water extraction and flow unevenness between units of each station as constraints. The original model is decomposed into several sub-models with a single station multi-objective optimization operation with the target water lifting capacity of a single pump station as the coordinating variable. This constructed model was solved using a large-scale system decomposition dynamic programming aggregation method based on sub-system multi-objective genetic algorithm optimization. Taking the Jiangdu parallel pumping station group in the Chinese East Route of the South-to-North Water Diversion Project as a case study, the results show that under the condition of 80% water lifting load of parallel stations and 7.8 m daily average lift, the unit water lifting cost of the optimal operation of each station decreases by 4.81%, 4.81%, 19.83% and 11.06% compared with the constant speed operation at the specified angle. The unevenness of the flow of each station is 2.16 m3/s, 2.16 m3/s, 0.60 m3/s and 14.10 m3/s. The erosion of the outlet pool is small. This article provides theoretical reference for the optimal operation of the same type of large-scale inter-basin water transfer parallel pumping station groups.

An optimization model for joint power generation dispatching of the cascade hydropower stations on the lower reaches of Jinsha River and the Yangtze River

The Xiluodu, Xiangjiaba, Three Gorges and Gezhouba cascade hydropower stations, which located at the lower reaches of Jinsha River and the upper reaches of Yangtze River, plays a very important role in the electrical power system in China. To optimize and solve the joint power generation problem of the cascade system with highly complex constraints, hydraulic relationship and multiple dispatching objectives, this research focus on: (1) a mid-and-long term power generation optimization model for the cascade system is established, considering hydraulic and electricty connections, as well as the flood control, water supply and ecology objectives; (2) an improved LSSDC-DDDP hybrid optimization framework, based on the theory of large-scale system decomposition coordination (LSSDC) and the discrete differential dynamic programming (DDDP), is designed to well solving the proposed optimization model. In the optimization framework, a relative coefficient is used to calculate the coordination factor among subsystems (a single hydropower station); meanwhile, an adaptive corridor and a bias corridor are adopted to enhance convergence speed of DDDP. The optimization model is applied in the dispatching calculation of the cascade system using the 2015-2017 actual runoff conditions, respectively. The results indicate that joint optimal dispatching of the cascade system can theoretically increase its yearly total power generation benefit about 2.73 billion yuan on average, simultaneously satisfying the requirements of downstream water supply and improving the total firm output guarantee rate of the system.

An ecological stability-oriented model for the conjunctive allocation of surface water and groundwater in oases in arid inland river basins

Abstract With the continuous development of the population and social economy, the spatial and temporal distribution of water resources in arid inland river basins is severely uneven, and there is a sharp contradiction between agricultural water use and ecological water use. Irrational development and utilization of water resources has led to many problems, such as shrinking oases and drying lakes. To solve this problem, this study proposes a multiobjective, multiwater-source, ecological stability-oriented double-layer model for optimal allocation of water resources based on the large-scale system decomposition–coordination principle, the water balance principle, and a water supply and demand forecasting model. This model can resolve the contradiction between agricultural water use and ecological water use by optimizing and adjusting the crop planting structure, industrial structure, and the amount of water allocated to and groundwater level in each region and thereby achieve ecological stability and restoration of oases. The developed model was applied to the Heihe River Basin in an inland region of Northwest China. The long-term time series data of 2000–2016 were used to construct and calibrate the model. Finally, the practical ecological stability-oriented plan for conjunctive allocation of surface water and groundwater in different plan years was proposed. This model enriches the research results related to the conjunctive allocation of surface water and groundwater and provides a reference for the ecological restoration of oases in arid inland river basins.

Multi-objective optimization scheduling of wind–photovoltaic–hydropower systems considering riverine ecosystem

Hydropower can aid in compensating for wind and photovoltaic power output fluctuations and uncertainties. In this study, a multi-objective optimization model was established by integrating wind and photovoltaic power with hydropower scheduling considering the total power generation, power output stability, and influence of hydropower on a downstream riverine ecosystem. An improved adaptive reference point-based multi-objective evolutionary algorithm was employed to solve the wind–photovoltaic–hydropower system problem with various complicated constraints. Moreover, the large-scale system decomposition principle was used to decouple a wind–photovoltaic–hydropower system into a wind–photovoltaic compensated subsystem and a hydropower system. A combined solution method was developed according to the subsystem characteristics to improve the model efficiency. Considering that direct crossover and mutation of hydropower systems may not yield feasible solutions, dynamic feasible regions for crossover and mutation were constructed for multi-objective optimal scheduling. Furthermore, a stochastic multi-criteria decision making model that accounts for the uncertainty of criterion information was established, and the non-dominated solution obtained using the improved multi-objective evolutionary algorithm was employed for decision-making. The results showed that the total power generation, power output stability, and downstream riverine ecosystem have strong competitive relationships, and the improved adaptive reference point-based multi-objective evolutionary algorithm can produce superior quality Pareto optimal solutions with uniform distribution. Subsequently, the stochastic multi-criteria decision making model was used to rank the Pareto optimal solutions, where each solution can obtain several ranks with different probabilities, providing extensive information for use in decision-making.

不同类型水电站群优化调度模型的大系统分解协调法研究

根据串并联水电站、混联水电站等不同类型水电站群的特点，建立了以发电量最大为目标的优化调度模型，模型同时考虑了水电站群间水力联系、电力联系等影响因素。针对不同类型水电站群优化调度模型构建了大系统分解协调算法，分别对模型问题分解、协调算法和收敛条件进行了详细的说明与推导。以清江流域水布垭、隔河岩、高坝洲水电站为例，建立了考虑梯级间流量传播影响和电力联系的3级串联水电站优化调度的大系统分解协调模型，大系统分解协调算法较传统算法计算效率更高，可以为大流域跨省区的复杂并联、混联水电站群多目标优化调度模型的构建、问题分解、以及算法等方面提供参考。 According to the characteristics of different types of hydropower stations such as cascade and parallel hydropower stations, and mixed hydropower stations, the optimal dispatching model with the largest generating capacity was established. The model considers the influencing factors such as hydraulic connection and power connection between hydropower stations. A large system decomposition and coordination algorithm was used for the optimal scheduling model of different types of hydropower stations. The problem decomposition, coordination algorithm and convergence conditions were described and deduced respectively. A large-scale system decomposition and coordination model of three-stage cascade hydropower station considering the influence of the flow rate between the steps and the power connection was established, taking the Shuibuya, Geheyan and Gaobazhou hydropower stations in the Qingjiang River basin as an example. The proposed method is more efficient than the traditional algorithm, which can provide reference for the complex parallelization of the inter-provincial provinces in the large watershed, the construction of the multi-objective optimal dispatching model of the hybrid hydropower station group, the problem decomposition, and the algorithm.

Decomposition of Enterprise Application: A Systematic Literature Review and Research Outlook

Enterprise applications are aimed at managing en- terprise operational data and improving business efficiency. Many enterprise applications have been developed over the past three decades, therefore, known as legacy systems. Usually, they are monolith, inflexible, poorly documented and hard to main- tain. The purpose of this paper is to describe best practices and limitations for enterprise application decomposition based on the results of the systematic literature review in order to introduce an approach for enterprise application decomposition. The paper focuses on decomposition of large-scale systems using clustering methods. The investigation is performed as part of the university- industry collaboration research project.

A Study on the Large-scale System Decomposition—Coordination Method Used in Optimal Operation of a Hydroelectric System

The optimal operation problem of multiple hydroelectric reservoir systems is very complex because of the large dimensions. Large-scale system decomposition-coordination methods, which can simplify complex problems into several interrelated sub-problems to avoid the “curse of dimensionality” and to obtain the global optimum on the global through coordination among sub-systems, is particularly well suited for optimizing large-scale, multi-reservoir systems. Applying this kind of theory and method, this paper studies and analyzes the problems of optimal operation of multiple hydroelectric reservoir systems in series, and sets up the optimal operation model of hydroelectric reservoir systems in series. On this basis, a practical example of two hydroelectric reservoirs in series on the upper reaches of the Yellow River in China is calculated and analyzed and the results are satisfactory. It is believed that applying this model can cut down the dimensions of the problem notably and that the theory and method are effective for real time operation.

Matrix scaling for large-scale system decomposition

Many large-scale systems exhibit the structure of weakly connected components. In such cases, proper identification of weakly coupled subsystems will add insight into large-scale system behavior, and aid in related tasks such as the design of decentralized control, ϵ-decomposition is a well-known efficient graph-theoretic algorithm for achieving a complete set of nested decompositions of a large-scale system. This paper shows how system matrix scaling can affect these decompositions, and determines that a system is properly scaled for ϵ-decomposition when it is max-balanced, a property associated with weighted directed graphs. Also, it is shown that an existing algorithm for max-balancing can be altered slightly to return the complete set of ϵ-decompositions, thus removing the need for two separate algorithms. Finally, the advantages of max-balancing before decomposition are shown for the application of decentralized control subsystem identification.

A hierarchical, multi-objective approach to the analysis, design, and selection of computer-integrated manufacturing systems

This paper develops a hierarchical, multi-objective programming framework for decision support, analysis, and design of computer-integrated manufacturing (CIM) systems. We demonstrate that each component of CIM, and CIM as a whole, is associated with conflicting objectives such as maximizing quality, profit, productivity, and flexibility. Realizing these objectives and finding appropriate ways to state and resolve their conflicts can play a major role in the development of CIM systems. We begin with an overview of hierarchical decision making as related to the time domain, and some important components of CIM as related to automation. We then relate manufacturing databases and the structure of decision support systems considering multiple and conflicting objectives. A hierarchical multi-objective framework, based on vertical and horizontal interdependencies, is then developed for analysis and design of CIM. The methodology is intended for decomposition of large-scale systems into a series of independent, multi-objective problems; we develop and illustrate an interactive approach to solve the decomposed problems and resolve the vertical and horizontal interdependencies. Finally, an approach for the selection of hardware/software systems for CIM is discussed and illustrated. Several examples are presented.

Cost Decomposition of Large-Scale Systems and Scaling of Input and Output Variables

A cost decomposition technique whose range of application goes beyond that of known dominance measures, participation matrices or component cost methods is presented. The approach consists of a four-dimensional array whose elements express the cost of each output-state-mode-input coupling. Such a wealth of information can be combined in many ways to provide either the dominance of various three or two-dimensional couplings or the participation of the individual outputs, states, modes or inputs in the output energy. The method lends itself ideally to model reduction, control structure selection or model structure analysis. Since cost decomposition techniques depend highly on the choice of units for the input and output variables, a scaling of input and output variables based on physical arguments is also presented and tested on simple models.

Separation of matrix eigenvalues and structural decomposition of large-scale systems

Separation of matrix eigenvalues and structural decomposition of large-scale systems

Two-Level Linear Programming

Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large-scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice. Multilevel programming models partition control over decision variables among ordered levels within a hierarchical planning structure. A planner at one level of the hierarchy may have his objective function and set of feasible decisions determined, in part, by other levels. However, his control instruments may allow him to influence the policies at other levels and thereby improve his own objective function. This paper examines the special case of the two-level linear programming problem. Geometric characterizations and algorithms are presented with some examples. The goal is to demonstrate the tractability of such problems and motivate a wider interest in their study.

Dynamic Modelling of Large Scale Systems

The decomposition of large scale systems into subsystems is discussed with respect to simulation model. The results are given in the form of the algorithm for building up of a simulation model with nonlinearities and constrains. The described approach was tested in simulation models of gas distribution networks and system of water channels.

On the attractivity of imbedded systems

A new approach designed to aid in the construction of Liapunov functions is proposed. It is based on the notion of partial properties. A given dynamic system is imbedded into an augmented system whose attractivity with respect to a part of variables is deduced by means of an auxiliary function. This leads to an exact procedure for computation of attractivity region estimates for dynamic systems. An important feature of the method is the great reduction of conservativeness of the region estimate in the case of the overlapping decomposition of large-scale systems. When applied to a multimachine power system with non-uniform damping and transfer conductances, the method gives an enlarged estimate of the region of transient stability.

On structure and stability of interconnected dynamical systems

In some recent works, graph-theoretic decomposition techniques were used in the stability analysis of large-scale interconnected dynamical systems. These results are applicable to systems with separable interconnecting structure. (By this term, we mean systems whose interconnecting structure enters additively into the system description and each term in the interconnecting structure connects at most two subsystems.) In this paper, we present results which are less conservative than the Lyapunov stability results developed previously and which are applicable to systems with nonseparable interconnecting structure. The graph-theoretic methods developed herein can be used to extend existing input-output stability results to be applicable to systems with nonseparable interconnecting structure as well. In arriving at the present results, generalizations of the usual concepts of a graph and a digraph (called a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> -graph and an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -digraph, respectively) are introduced, and some of their properties are established. These graphtheoretic results, which we feel are of interest in their own right, make possible the systematic decomposition of large-scale systems into several useful and important equivalent forms. Indeed, these decomposition results constitute generalizations of earlier ones which use the usual notion of a digraph. To clarify concepts introduced and to demonstrate the usefulness of the results developed, several specific examples are included in the paper.

On the decomposition of large-scale systems of linear algebraic equations

On the decomposition of large-scale systems of linear algebraic equations

Parametric solution to the joint system identification and optimization problem

This study is concerned with the simultaneous identification and optimization of static systems. The necessity and the advantages of an integrated approach to the identification and optimization of the system model is established theoretically as well as computationally. A parametric approach to the integrated problem is proven to converge to the integrated problem solution. The general methodology of decomposition of large-scale systems is extended by implementingfeasible decomposition of the joint problem. A multilevel approach is then utilized to successfully solve example problems. Handling the system constraints via a penalty-function technique is shown to be an efficient approach when using the parametric formulation of the joint problem. Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.

OPTIMAL DESIGN OF A CHEMICAL REACTOR WITH FAST AND SLOW REACTIONS

Abstract Singular perturbation methods, developed originally by Levin and Levinson (1954) and Vasil'eva (1963), can be viewed as an alternative technique for decomposition of large-scale systems with widely-varying time constants. An example is a chemical reactor in which a multiplicity of fast and slow chemical reactions simultaneously occur. A lower-order model frequently adopted to simplify the calculations, may not be completely adequate, and a singular perturbation attack offers an efficient correction procedure. It is found that the optimal design is quite sensitive to small changes in some of the feed components, but not to others.