scholarly journals Optimal Operation of a Single Unit with an Adjustable Blade in an Interbasin Water Transfer Pumping Station Based on Successive Approximation Discretization for Blade Angle

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yi Gong ◽  
Jilin Cheng ◽  
Li Che ◽  
Liang Wang ◽  
Zaiyang Chen ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Dynamic Programming ◽  
Successive Approximation ◽  
Single Unit ◽  
Optimal Operation ◽  
Feasible Region ◽  
Blade Angle ◽  
Pump Unit ◽  
Step Size ◽  
Water Pumping

In the mathematical model of the optimal operation of a single pump unit with a fully adjustable blade in the Chinese South-to-North Water Diversion Project, the decision variable, namely, blade angle, was uniformly dispersed in its feasible region in a fixed step size in consideration of the requirements of the pumping head and matching motor power. 1D dynamic programming was applied to solve the original model. When the obtained blade for each time period was set as the middle reference value and the discrete region of the blade was reduced to two times of the step size in the previous time, the blade angle was correspondingly reduced and dispersed in this new discrete region, thus eliminating unnecessary optimization space. Then, 1D dynamic programming was applied again to optimize the blade angle of the single pump unit further. After a series of successive approximation discretization of the blade angle and corresponding solutions of the obtained mathematical model, the optimization process was considered completed when the given control precision met the requirement. A case study showed that under typical operating conditions, the total cost saving percentage of water pumping quantity reached 0.048%–0.463%, with an average saving rate of 0.192%. The actual total water pumping quantity of the single unit decreased by 2153 m3 on the average. The proposed discretization method exerted a better optimization effect and needed a smaller computational amount compared with traditional one-time uniform discretization in the original feasible region of the blade angle.

scholarly journals Combinatorial Optimization Method for Operation of Pumping Station with Adjustable Blade and Variable Speed Based on Experimental Optimization of Subsystem

2014 ◽  
Vol 6 ◽  
pp. 283520 ◽  
Author(s):  
Yi Gong ◽  
Jilin Cheng
Keyword(s):  
Dynamic Programming ◽  
Optimal Operation ◽  
Constant Speed ◽  
Water Quantity ◽  
Decision Variable ◽  
Variable Speed ◽  
Pump Unit ◽  
Experimental Optimization ◽  
Pumping Station ◽  
Discrete Values

A decomposition-dynamic programming aggregation method based on experimental optimization for subsystem was proposed to solve mathematical model of optimal operation for single pumping station with adjustable blade and variable speed. Taking minimal daily electric cost as objective function and water quantity pumped by units as coordinated variable, this model was decomposed into several submodels of daily optimal operation with adjustable blade and variable speed for single pump unit which was solved by experimental optimization. The constructed aggregation model took water quantity pumped by each pump unit as decision variable and discrete values of water quantity pumped by pumping station as state variable and was solved by one-dimensional dynamic programming. Taking operation of typical pumping station as a study case, optimal operation with adjustable blade and variable speed, respectively, had an average cost saving of 4.19%, 22.15%, and 29.86% compared with operation with fixed blade angle and constant speed under 100%, 80%, and 60% load, which also had a remarkable saving amplitude of 15.85% and 24.18%, respectively, corresponding to 80% load and 60% load compared with operation with adjustable blade and constant speed. Meanwhile, the proposed method has provided a new way for solving complex nonlinear mathematical models with 3 decision variables.

scholarly journals Combined Aggregated Sampling Stochastic Dynamic Programming and Simulation-Optimization to Derive Operation Rules for Large-Scale Hydropower System

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 625
Author(s):  
Xinyu Wu ◽  
Rui Guo ◽  
Xilong Cheng ◽  
Chuntian Cheng
Keyword(s):  
Dynamic Programming ◽  
Stochastic Dynamic Programming ◽  
Large Scale ◽  
Simulation Optimization ◽  
Optimal Operation ◽  
Stochastic Dynamic ◽  
Operation Model ◽  
Two Stage ◽  
Operation Rules ◽  
Reservoir Systems

Simulation-optimization methods are often used to derive operation rules for large-scale hydropower reservoir systems. The solution of the simulation-optimization models is complex and time-consuming, for many interconnected variables need to be optimized, and the objective functions need to be computed through simulation in many periods. Since global solutions are seldom obtained, the initial solutions are important to the solution quality. In this paper, a two-stage method is proposed to derive operation rules for large-scale hydropower systems. In the first stage, the optimal operation model is simplified and solved using sampling stochastic dynamic programming (SSDP). In the second stage, the optimal operation model is solved by using a genetic algorithm, taking the SSDP solution as an individual in the initial population. The proposed method is applied to a hydropower system in Southwest China, composed of cascaded reservoir systems of Hongshui River, Lancang River, and Wu River. The numerical result shows that the two-stage method can significantly improve the solution in an acceptable solution time.

scholarly journals Dynamic Operation Management of a Renewable Microgrid including Battery Energy Storage

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Shaozhen Jin ◽  
Zhizhong Mao ◽  
Hongru Li ◽  
Wenhai Qi
Keyword(s):  
Dynamic Programming ◽  
Energy Storage ◽  
Renewable Energy Sources ◽  
Main Idea ◽  
Optimal Operation ◽  
Optimal Control Strategy ◽  
Programming Technique ◽  
Battery Energy Storage ◽  
Comparison Results ◽  
Battery Energy

In this paper, a novel dynamic programming technique is presented for optimal operation of a typical renewable microgrid including battery energy storage. The main idea is to use the scenarios analysis technique to proceed the uncertainties related to the available output power of wind and photovoltaic units and dynamic programming technique to obtain the optimal control strategy for a renewable microgrid system in a finite time period. First, to properly model the system, a mathematical model including power losses of the renewable microgrid is established, where the uncertainties due to the fluctuating generation from renewable energy sources are considered. Next, considering the dynamic power constraints of the battery, a new performance index function is established, where the Lagrange multipliers and interior point method will be presented for the equality and inequality operation constraints. Then, a feedback control scheme based on the dynamic programming is proposed to solve the model and obtain the optimal solution. Finally, simulation and comparison results are given to illustrate the performance of the presented method.

scholarly journals The treatment of optimizing container transportation dynamic programming and planning

2019 ◽  
Vol 135 ◽  
pp. 02016
Author(s):  
Elena Korchagina ◽  
Andrey Bochkarev ◽  
Pavel Bochkarev ◽  
Sergey Barykin ◽  
Svetlana Suvorova
Keyword(s):  
Mathematical Model ◽  
Dynamic Programming ◽  
Linear Programming ◽  
Numerical Calculation ◽  
Optimal Strategy ◽  
Programming Algorithm ◽  
Container Transportation ◽  
Dynamic Planning ◽  
Railway Freight ◽  
Linear Programming Algorithm

The article addresses the treatment of applying the method of dynamic linear programming to solve the task of choosing the optimal strategy for the containers dispatch, taking into account the significant unevenness of loading and shipment of containers. The optimizing container transportation dynamic planning could be treated as mathematical model of the dynamic multi-period task of the loaded containers shipment, which allows the choice of the optimal strategy for sending containers, taking into account the significant unevenness of their loading and dispatch from the railway freight station. The efficiency of considered method is proved by numerical calculation being presented to disclose the dynamic linear programming algorithm implementing to solve the problem.

GLOBAL DYNAMICS OF A MATHEMATICAL MODEL OF TUBERCULOSIS WITH AGE-DEPENDENT LATENCY AND ACTIVE INFECTION

2019 ◽  
Vol 27 (04) ◽  
pp. 503-530
Author(s):  
RUI XU ◽  
NING BAI ◽  
XIAOHONG TIAN
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Feasible Region ◽  
Global Dynamics ◽  
Active Infection ◽  
Age Dependent ◽  
Latent Tb ◽  
Latent Tb Infection ◽  
The Basic Reproduction Number

In this paper, mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) with age-dependent latency and active infection. The model divides latent TB infection into two stages: an early stage of high risk of developing active TB and a late stage of lower risk for developing active TB. Infected persons initially progress through the early latent TB stage and then can either progress to active TB infection or progress to late latent TB infection. The model is formulated by incorporating the duration that an individual has spent in the stages of the early latent TB, the late latent TB and the active TB infection as variables. By constructing suitable Lyapunov functionals and using LaSalle’s invariance principle, it is shown that the global dynamics of the disease is completely determined by the basic reproduction number: if the basic reproduction number is less than unity, the TB always dies out; if the basic reproduction number is greater than unity, a unique endemic steady state exists and is globally asymptotically stable in the interior of the feasible region and therefore the TB becomes endemic. Numerical simulations are carried out to illustrate the theoretical results.

Steering Strategy for a Multi-Axle Wheeled Vehicles

2018 ◽  
Author(s):  
Waqar Ahmed ◽  
Raja Amer Azim ◽  
Sana Fatima
Keyword(s):  
Mathematical Model ◽  
Single Unit ◽  
Steering System ◽  
Vehicle Speed ◽  
Wheel Slip ◽  
Turn Radius ◽  
Heavy Loads ◽  
The Mathematical Model ◽  
Wheeled Vehicles ◽  
Good Vehicle

This paper presents a mathematical model for multi-axle steering vehicles operating on level ground. For transporting heavy loads vehicles with multiple axles are required. Apart from added complexity steering of multiple axle for turning is a big challenge. Due to type of load being carried a single unit vehicle is sometimes preferred. The mathematical model of a six axle vehicle with 4-axle steering system is developed. Simulations at various track radii, vehicle speeds and steering ratios (ratio between the first, second, fifth and sixth steering axle) are performed. Axle steering angles and wheel slip angles are evaluated. The steering ratio requirements vary with vehicle speed and turn radius. A configuration is selected for better performance for a wider range. The resulting steering ratios show good vehicle maneuverability, stability and steering efficiency.

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