• Title/Summary/Keyword: vector equilibrium problem

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Optimal Bidding Strategy of Competitive Generators Under Price Based Pool (PBP(Price Based Pool) 발전경쟁시장에서의 최적입찰전략수립)

  • Kang, Dong-Joo;Hur, Jin;Moon, Young-Hwan;Chung, Koo-Hyung;Kim, Bal-Ho
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.51 no.12
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    • pp.597-602
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    • 2002
  • The restructuring of power industry is still going on all over the world for last several decades. Many kinds of restructuring model have been studied, proposed, and applied. Among those models, power pool is more popular than other. This paper assumes the power pool market structure having competitive generation sector, and a new method is presented to build a bidding strategy in that market. The utilities participating in the market have the perfect information of their cost and price functions, but they don't know which strategy to be chosen by others. To define one's strategy as a vector, we make utility's cost/price functions into discrete step functions. An utility knows only his own strategy, so he estimates the other's cost/price functions into discrete step functions. An utility knows only his own strategy, so he estimates the other's strategy using Nash equilibrium or stochastic methods. And he also has to forecast the system demand. According to this forecasting result, his payoffs can be changed. Considering these all conditions, we formulate a bidding game problem and apply noncooperative game theory to that problem for the optimal strategy or solution. Some restrictive assumption are added for simplification of solving process. A numerical example is given in Case Study to show essential features and concrete results of this approach.

A Genetic Algorithm for Trip Distribution and Traffic Assignment from Traffic Counts in a Stochastic User Equilibrium (사용자 평형을 이루는 통행분포와 통행배정을 위한 유전알고리즘)

  • Sung, Ki-Seok
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2006.11a
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    • pp.599-617
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    • 2006
  • A network model and a Genetic Algorithm(GA) is proposed to solve the simultaneous estimation of the trip distribution and traffic assignment from traffic counts in the congested networks in a logit-based Stochastic User Equilibrium (SUE). The model is formulated as a problem of minimizing the non-linear objective functions with the linear constraints. In the model, the flow-conservation constraints of the network are utilized to restrict the solution space and to force the link flows meet the traffic counts. The objective of the model is to minimize the discrepancies between the link flows satisfying the constraints of flow-conservation, trip production from origin, trip attraction to destination and traffic counts at observed links and the link flows estimated through the traffic assignment using the path flow estimator in the legit-based SUE. In the proposed GA, a chromosome is defined as a vector representing a set of Origin-Destination Matrix (ODM), link flows and travel-cost coefficient. Each chromosome is evaluated from the corresponding discrepancy, and the population of the chromosome is evolved by the concurrent simplex crossover and random mutation. To maintain the feasibility of solutions, a bounded vector shipment is applied during the crossover and mutation.

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Large deflection analysis of laminated composite plates using layerwise displacement model

  • Cetkovic, M.;Vuksanovic, Dj.
    • Structural Engineering and Mechanics
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    • v.40 no.2
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    • pp.257-277
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    • 2011
  • In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

Analysis of cable structures through energy minimization

  • Toklu, Yusuf Cengiz;Bekdas, Gebrail;Temur, Rasim
    • Structural Engineering and Mechanics
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    • v.62 no.6
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    • pp.749-758
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    • 2017
  • In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, $P=K{\Delta}$, where P is the load vector, K is the stiffness matrix and ${\Delta}$ is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of non-linear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate.

Topological Design Sensitivity on the Air Bearing Surface of Head Slider

  • Yoon, Sang-Joon;Kim, Min-Soo;Park, Dong-Hoon
    • Journal of Mechanical Science and Technology
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    • v.16 no.8
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    • pp.1102-1108
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    • 2002
  • In this study, a topological design sensitivity of the ai. bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.

Passivity-Based Control System of Permanent Magnet Synchronous Motors Based on Quasi-Z Source Matrix Converter

  • Cheng, Qiming;Wei, Lin
    • Journal of Power Electronics
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    • v.19 no.6
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    • pp.1527-1535
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    • 2019
  • Because of the shortcomings of the PID controllers and traditional drive systems of permanent magnet synchronous motors (PMSMs), a PMSM passivity-based control (PBC) drive system based on a quasi-Z source matrix converter (QZMC) is proposed in this paper. The traditional matrix converter is a buck converter with a maximum voltage transmission ratio of only 0.866, which limits the performance of the driven motor. Therefore, in this paper a quasi-Z source circuit is added to the input side of the two-stage matrix converter (TSMC) and its working principle has also been verified. In addition, the controller of the speed loop and current loop in the conventional vector control of a PMSM is a PID controller. The PID controller has the problem since its parameters are difficult to adjust and its anti-interference capability is limited. As a result, a port controlled dissipative Hamiltonian model (PCHD) of a PMSM is established. Thereafter a passivity-based controller based on the interconnection and damping assignment (IDA) of a QZMC-PMSM is designed, and the stability of the equilibrium point is theoretically verified. Simulation and experimental results show that the designed PBC control system of a PMSM based on a QZMC can make the PMSM run stably at the rated speed. In addition, the system has strong robustness, as well as good dynamic and static performances.

A Study on Regionalization in the World Crude Oil Markets Using Cointegration and Causality Analysis (공적분과 인과관계 분석을 통한 국제원유시장의 지역화 연구)

  • Kim, Jinsoo;Heo, Eunnyeong;Kim, Yeonbae
    • Environmental and Resource Economics Review
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    • v.16 no.2
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    • pp.213-237
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    • 2007
  • Discussions on regionalization of the world crude oil markets have provided important implications for the establishment of national energy policies. In particular, due to arbitrage trading, if these markets are regionalized, Korea who imports approximately 80% of the annual oil consumption from a single region may be faced with a crucial problem. Therefore, in this study, we analyzed regionalization of the world crude oil markets using causality analysis as well as cointegration method to consider temporal relationship and time lags. To analyze regionalization, we chose Dubai price for the Middle East market, Brent for the European, WTI for the U.S., and Tapis for the East Asian. For the case that long-run equilibrium existed between market prices, we used vector error correction model to analyze causal relationship, and for the case that equilibrium did not exist, we used Hsiao (1981)'s framework that can consider asymmetric time lags in the model for causality analysis. By the results of cointegration analysis, there did not exist long-run equilibrium among Dubai price and the other prices. However, we found the causal relationship among Dubai price and the other prices with one to four weeks time lags. Therefore, in effect, we could conclude that the world crude oil markets are unified supporting Adelman (1984)'s hypothesis.

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