Co-Optimization of Output and Reserve with Significant Penetration of Renewables

2013 ◽  
Vol 427-429 ◽  
pp. 341-345
Author(s):  
Xue Fei Chang ◽  
Zhe Yong Piao ◽  
Xiang Yu Lv ◽  
De Xin Li
Keyword(s):  
Quadratic Programming ◽  
Wind Power ◽  
Sequential Quadratic Programming ◽  
Renewable Generation ◽  
Renewable Sources ◽  
Reliability Level ◽  
Maximum Benefit ◽  
Proposed Model ◽  
Programming Techniques

Co-optimization of output and reserve is necessary in order to provide maximum benefit to both consumers and producers. Once renewable generation sources like wind or solar begin to make up a large proportion of the generation mix, this co-optimization becomes much more difficult since the output of renewable sources is not well-known in advance. In this paper, a uniform reliability level is used as a constraint in the process of output and reserve. The proposed model is tested on the modified 5-bus PJM system. The co-optimization is performed by sequential quadratic programming techniques. The results show that the co-optimization results are strongly related to the uncertainties of wind power, the reliability level of the system, and the reliability of generators when wind makes up a significant portion of the generation mix.

scholarly journals Sequential Quadratic Programming Method for Nonlinear Least Squares Estimation and Its Application

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengqing Fu ◽  
Goulin Liu ◽  
Lanlan Guo
Keyword(s):  
Quadratic Programming ◽  
Least Squares ◽  
Sequential Quadratic Programming ◽  
Mean Squared Error ◽  
Programming Model ◽  
Nonlinear Least Squares ◽  
Least Squares Estimation ◽  
Estimation Model ◽  
Proposed Model ◽  
Nonlinear Least Squares Estimation

In this study, we propose a direction-controlled nonlinear least squares estimation model that combines the penalty function and sequential quadratic programming. The least squares model is transformed into a sequential quadratic programming model, allowing for the iteration direction to be controlled. An ill-conditioned matrix is processed by our model; the least squares estimate, the ridge estimate, and the results are compared based on a combination of qualitative and quantitative analyses. For comparison, we use two equality indicators: estimated residual fluctuation of different methods and the deviation between estimated and true values. The root-mean-squared error and standard deviation are used for quantitative analysis. The results demonstrate that our proposed model has a smaller error than other methods. Our proposed model is thereby found to be effective and has high precision. It can obtain more precise results compared with other classical unwrapping algorithms, as shown by unwrapping using both simulated and real data from the Jining area in China.

Design of evolutionary cubic spline intelligent solver for nonlinear Painlevé-I transcendent

2021 ◽  
Author(s):  
Sharafat Ali ◽  
Iftikhar Ahmad ◽  
Muhammad Asif Zahoor Raja ◽  
Siraj ul Islam Ahmad ◽  
Muhammad Shoaib
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Genetic Algorithms ◽  
Statistical Analysis ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Process Variation ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Derivative ◽  
Search Technique

In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic splines method (CSM) has been utilized to estimate the numerical results of nonlinear ordinary differential equation Painlevé-I. The computational mechanism is used to support the proposed technique CSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick refinement. Painlevé-I is solved by the proposed technique CSM-GASQP. In this process, variation of splines is implemented for various scenarios. The CSM-GASQP produces an interpolated function that is continuous upto its second derivative. Also, splines proved to be stable than a single polynomial fitted to all points, and reduce wiggles between the tabulated points. This method provides a reliable and excellent procedure for adaptation of unknown coefficients of splines by searching globally exploiting the performance of GA-SQP algorithms. The convergence, exactness and accuracy of the proposed scheme are examined through the statistical analysis for the several independent runs.

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