American Institute of Mathematical Sciences

Advanced
October  2008, 4(4): 673-684. doi: 10.3934/jimo.2008.4.673

Dynamic power price problem: An inverse variational inequality approach

Junfeng Yang 1,

1. 

Department of Mathematics, Nanjing University, Nanjing, 210093, China

Received  March 2007 Revised  April 2008 Published  November 2008

This paper considers an optimal control perspective on dynamic power price problem where the load on the power-grid is controlled via price. The optimal regulatory price is characterized by inverse variational inequality in which the function value and the control variable are in the opposite positions of the classical variational inequality. Discrete and continuum models with load constraints are developed and existence theorems are established under quite reasonable assumptions. Preliminary numerical results also show the feasibility of the proposed models.
Keywords: load constraint, dynamic power price, power-grid., Inverse variational inequality.
Mathematics Subject Classification: 49J20, 49J40, 90B5.
Citation: Junfeng Yang. Dynamic power price problem: An inverse variational inequality approach. Journal of Industrial & Management Optimization, 2008, 4 (4) : 673-684. doi: 10.3934/jimo.2008.4.673
[1]

Ming Chen, Chongchao Huang. A power penalty method for a class of linearly constrained variational inequality. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1381-1396. doi: 10.3934/jimo.2018012
[2]

Takeshi Fukao. Variational inequality for the Stokes equations with constraint. Conference Publications, 2011, 2011 (Special) : 437-446. doi: 10.3934/proc.2011.2011.437
[3]

Yeming Dai, Yan Gao, Hongwei Gao, Hongbo Zhu, Lu Li. A real-time pricing scheme considering load uncertainty and price competition in smart grid market. Journal of Industrial & Management Optimization, 2020, 16 (2) : 777-793. doi: 10.3934/jimo.2018178
[4]

Chuong Van Nguyen, Phuong Huu Hoang, Hyo-Sung Ahn. Distributed optimization algorithms for game of power generation in smart grid. Numerical Algebra, Control & Optimization, 2019, 9 (3) : 327-348. doi: 10.3934/naco.2019022
[5]

Guillaume Bal, Eric Bonnetier, François Monard, Faouzi Triki. Inverse diffusion from knowledge of power densities. Inverse Problems & Imaging, 2013, 7 (2) : 353-375. doi: 10.3934/ipi.2013.7.353
[6]

Mohammed Al-Azba, Zhaohui Cen, Yves Remond, Said Ahzi. Air-Conditioner Group Power Control Optimization for PV integrated Micro-grid Peak-shaving. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3165-3181. doi: 10.3934/jimo.2020112
[7]

Liping Pang, Fanyun Meng, Jinhe Wang. Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1653-1675. doi: 10.3934/jimo.2018116
[8]

Takeshi Fukao, Nobuyuki Kenmochi. Quasi-variational inequality approach to heat convection problems with temperature dependent velocity constraint. Discrete & Continuous Dynamical Systems, 2015, 35 (6) : 2523-2538. doi: 10.3934/dcds.2015.35.2523
[9]

Reetabrata Mookherjee, Benjamin F. Hobbs, Terry L. Friesz, Matthew A. Rigdon. Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints. Journal of Industrial & Management Optimization, 2008, 4 (3) : 425-452. doi: 10.3934/jimo.2008.4.425
[10]

Hongming Yang, C. Y. Chung, Xiaojiao Tong, Pingping Bing. Research on dynamic equilibrium of power market with complex network constraints based on nonlinear complementarity function. Journal of Industrial & Management Optimization, 2008, 4 (3) : 617-630. doi: 10.3934/jimo.2008.4.617
[11]

Noriyoshi Fukaya. Uniqueness and nondegeneracy of ground states for nonlinear Schrödinger equations with attractive inverse-power potential. Communications on Pure & Applied Analysis, 2021, 20 (1) : 121-143. doi: 10.3934/cpaa.2020260
[12]

Joseph Bayara, André Conseibo, Artibano Micali, Moussa Ouattara. Derivations in power-associative algebras. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1359-1370. doi: 10.3934/dcdss.2011.4.1359
[13]

Marilena Filippucci, Andrea Tallarico, Michele Dragoni. Simulation of lava flows with power-law rheology. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 677-685. doi: 10.3934/dcdss.2013.6.677
[14]

Daniel Mckenzie, Steven Damelin. Power weighted shortest paths for clustering Euclidean data. Foundations of Data Science, 2019, 1 (3) : 307-327. doi: 10.3934/fods.2019014
[15]

Xiaojiao Tong, Felix F. Wu, Yongping Zhang, Zheng Yan, Yixin Ni. A semismooth Newton method for solving optimal power flow. Journal of Industrial & Management Optimization, 2007, 3 (3) : 553-567. doi: 10.3934/jimo.2007.3.553
[16]

Juan Pablo Cárdenas, Gerardo Vidal, Gastón Olivares. Complexity, selectivity and asymmetry in the conformation of the power phenomenon. Analysis of Chilean society. Networks & Heterogeneous Media, 2015, 10 (1) : 167-194. doi: 10.3934/nhm.2015.10.167
[17]

Hironobu Sasaki. Remark on the scattering problem for the Klein-Gordon equation with power nonlinearity. Conference Publications, 2007, 2007 (Special) : 903-911. doi: 10.3934/proc.2007.2007.903
[18]

Van Duong Dinh, Binhua Feng. On fractional nonlinear Schrödinger equation with combined power-type nonlinearities. Discrete & Continuous Dynamical Systems, 2019, 39 (8) : 4565-4612. doi: 10.3934/dcds.2019188
[19]

Kai Zhang, Xiaoqi Yang, Song Wang. Solution method for discrete double obstacle problems based on a power penalty approach. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021018
[20]

Johan Rosenkilde. Power decoding Reed-Solomon codes up to the Johnson radius. Advances in Mathematics of Communications, 2018, 12 (1) : 81-106. doi: 10.3934/amc.2018005

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (76)
  • HTML views (0)
  • Cited by (19)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences