Robust optimal operation of continuous catalytic reforming process under feedstock uncertainty

This paper presents a new approach aims to solve robust multidisciplinary design optimization MDO problem called Improved Multi-objective Robust Collaborative Optimization . This method combines the Multi-objective Robust Collaborative Optimization method, the Worst Possible Point constraint cuts and the Genetic algorithm NSGA-II type as an optimizer to solve the robust optimization problem of complex structure named Y-stiffened panel under interval uncertainty . The proposed approach hierarchically decomposes the optimization problem into a structure level considered as an upper level in the Y-stiffened panel and a second level considered as a lower level of the studied panel. A robust multi-objective optimization problem intended to optimize the eigenfrequency, the global mass and the displacement at a fixed point of the Y-stiffened panel at the first level and each structure’s robust optimization problem allows optimizing its eigenfrequency and mass limited by their local constraint functions at the second one. Tor demonstrate our method, an engineering example of Y-stiffened panel is treated. A good performance of proposed method is proved by a comparison between obtained results and Non-Distributed Multi-objective Robust Optimization .

Multi-objective robust dynamic pricing and operation strategy optimization for integrated energy system based on stackelberg game

The multi energy complementary system is a new power energy technology Firstly, we studied renewable energy and load uncertainties of an operation optimization system, and established the industrial park energy system, which includes wind power, photovoltaic power, a combined cooling, heating and power system, and an energy storage tank. Secondly, given the renewable energy uncertainties of unit output and load, we introduced a robust multi-objective operation optimization method for industrial park energy supply systems while considering conservative system operation. Thirdly, we examined the synergetic and game relationship among multiple objectives. The particle swarm optimization algorithm is was used to optimize the system operation scheme, reduce the feasible domain, and improve the efficiency of the solution. Finally, the simulation results show that the operation optimization method effectively uses the demand response to optimize economic and environmental objectives and ensure the optimal operation efficiency of the system under multiple uncertainties.

Surrogate duality for robust optimization

With the gradual increase of distributed energy penetration, the traditional optimization model of distribution network can no longer guarantee the stable and efficient operation of the distribution network. In order to deal with the inevitable uncertainty of distributed energy, a new robust optimal operation method is proposed for active distribution network (ADN) based on the minimum confidence interval of distributed energy Beta distribution in this paper. First, an ADN model is established with second-order cone to include the energy storage device, capacitor bank, static var compensator, on-load tap changer, wind turbine and photovoltaic. Then, the historical data of related distributed energy are analyzed and described by the probability density function, and the minimum confidence interval is obtained by interval searching. Furthermore, via taking this minimum confidence interval as the uncertain interval, a less conservative two-stage robust optimization model is established and solved for ADN. The simulation results for the IEEE 33-bus distribution network have verified that the proposed method can realize a more stable and efficient operation of the distribution network compared with the traditional robust optimization method.

Mars entry trajectory planning using robust optimization and uncertainty quantification

Fast robust optimization of ORC based on an artificial neural network for waste heat recovery

Due to the strong coupling relationship between active power and reactive power in distribution network, the traditional method of optimizing the active and reactive power cannot make the distribution network operate in the optimal state of economical operation. And the uncertainties of load demand and power of distributed generation bring great challenges to the operation of distribution network. Based on this, a two-stage robust economical operation optimization method for distribution network considering multiple adjustment measures, including on-load tap changer, capacitor banks, static var compensator, electrical storage system and switch reconfiguration, is proposed on the basis of the branch power flow model. And the non-linear power flow constraint is relaxed by second order cone so that the economical operation optimization model is transformed into the mixed integer second order conic programming model to solve effectively. To solve the uncertainties of load demand and power of distributed generation, two-stage robust optimization method is adopted, and the optimal robust operation strategy of each adjustment measure is obtained through the column and constraint generation algorithm. Finally, the validity of the proposed model is verified by IEEE 33 bus system.

The distribution grid experiences node voltage fluctuations due to the growing uncertainty of large-scale renewable energy sources A practical solution is establishing a chance-constrained optimal model to deal with the uncertainties. However, using this method needs to know the accurate probability distribution of node power injections, which has limitations in application. Therefore, this paper proposes a distributionally robust chance-constrained optimization method for power grid operation based on the ambiguity set of probability distributions. Firstly, considering voltage security constraints, this paper establishes a chance-constrained model to minimize the cost of active power regulation. Besides, based on the Wasserstein ambiguity set, a linearized method is proposed to convexify the objective function. Moreover, the conditional risk value (CVaR) is applied to convert the uncertain model into a deterministic model. The effectiveness of the proposed method is validated through optimization results obtained for the modified PG&E69-bus distribution grid.

Chapter 4 - Data-driven robust stochastic optimization for power systems operations

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

A review on cooling performance enhancement for phase change materials integrated systems—flexible design and smart control with machine learning applications

microgrids (MGs) are a promising solution to global energy challenges. Robust and reliable operation while maximizing infeed from renewable sources and reducing the use of thermal generation are important objectives in the control of MGs. In this paper, two model predictive control strategies are applied to operate a grid-connected MG in the presence of bounded uncertainties in an optimal way. One is a certainty-equivalence and the other a minimax approach. They differ in the disturbance model used for renewable energy source infeed and load. To find an optimal operation strategy, a mixed-integer quadratic program is solved online. In a numerical case study, the results of two approaches are analyzed. The simulation shows, that compared to the performance of the certainty-equivalent case, the minimax approach is robust to disturbances and allows a secure operation of MGs in grid-connected mode.

Some optimal operation methods based on the mixed-integer linear programming (MILP) have been proposed to operate energy supply plants properly from the viewpoints of economics, energy saving, and CO2 emission reduction. However, most of the methods are effective only under certain energy demands. In operating an energy supply plant actually, it is necessary to determine the operational strategy properly based on predicted energy demands. In this case, realized energy demands may differ from the predicted ones. Therefore, it is necessary to determine the operational strategy so that it is robust against the uncertainty in energy demands. In this paper, an optimization method based on the MILP is proposed to conduct the robust optimal operation of energy supply plants under uncertain energy demands. The uncertainty in energy demands is expressed by their intervals. The operational strategy is determined to minimize the maximum regret in the operational cost under the uncertainty. In addition, a hierarchical relationship among operation modes and on/off states of equipment, energy demands, and energy flow rates of equipment is taken into account. First, a general formulation of a robust optimal operation problem is presented, which is followed by a general solution procedure. Then, in a numerical study, the proposed method is applied to a gas turbine cogeneration plant for district energy supply. Through the study, some features of the robust optimal operation are clarified, and the validity and effectiveness of the proposed method are ascertained.

Some optimal operation methods based on the mixed-integer linear programming have been proposed to operate energy supply plants properly from the viewpoints of economics, energy saving, and CO2 emission reduction. However, most of the methods are effective only under certain energy demands. In operating an energy supply plant actually, it is necessary to determine the operational strategy properly based on predicted energy demands. In this case, realized energy demands may differ from the predicted ones. Therefore, it is necessary to determine the operational strategy so that it is robust against the uncertainty in energy demands. In this paper, an optimization method based on the mixed-integer linear programming is proposed to conduct the robust optimal operation of energy supply plants under uncertain energy demands. The uncertainty in energy demands is expressed by their intervals. The operational strategy is determined to minimize the maximum regret in the operational cost under the uncertainty. In addition, a hierarchical relationships among operation modes and on/off states of equipment, energy demands, and energy flow rates of equipment are taken into account. First, a general formulation of a robust optimal operation problem is presented, which is followed by a general solution procedure. Then, in a numerical study, the proposed method is applied to a gas turbine cogeneration plant for district energy supply. Through the study, some features of the robust optimal operation are clarified, and the validity and effectiveness of the proposed method are ascertained.