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Exploiting the Flexibility Value of Virtual Power Plants through Market Participation in Smart Energy Communities
Published in Ehsan Heydarian-Forushani, Hassan Haes Alhelou, Seifeddine Ben Elghali, Virtual Power Plant Solution for Future Smart Energy Communities, 2023
Georgios Skaltsis, Stylianos Zikos, Elpiniki Makri, Christos Timplalexis, Dimosthenis Ioannidis, Dimitrios Tzovaras
There are different types of optimization algorithms which can be categorized based on the nature of the variables (continuous or discrete) or based on the constraints (linear or nonlinear). Hereinafter, the derived main categories are linear programming (LP), mixed-integer linear programming (MILP), nonlinear programming and mixed-integer nonlinear programming. In LP, the objective functions as much as the set of the constraints on the decision variables are linear. Simplex method, a quite common LP algorithm, involves a linear function and several constraints are expressed as inequalities. This algorithm is generating and examining candidate vertex solutions and usually requires a negligible time to find the optimal one. Moreover, the column generation method is a technique which is utilized for solving MILP problems in case of a large number of variables in comparison with the number of constraints. This method is effective, considering the fact that it avoids enumerating all the possible elements like any traditional MILP algorithm. On the other hand, quadratic programming problems are a simple form of nonlinear problems, consisting of a convex or non-convex quadratic function of variables.
Introduction
Published in Laxmidhar Behera, Swagat Kumar, Prem Kumar Patchaikani, Ranjith Ravindranathan Nair, Samrat Dutta, Intelligent Control of Robotic Systems, 2020
Laxmidhar Behera, Swagat Kumar, Prem Kumar Patchaikani, Ranjith Ravindranathan Nair, Samrat Dutta
Techniques have been developed to find the optimal solution of the non-convex problems. Interior-point methods, active-set techniques, sequential quadratic programming, etc., [118–120] are quite efficient and fast to find solutions which are locally optimal. Being local optimization techniques, these approaches end up as different solutions with different initial guesses. The chances of finding the global optima is high if the initial guess is close to the global optima. On the other hand genetic algorithm (GA) [121, 122], particle swarm optimization [123], and simulated annealing [124] reaches global optima (ideally) given a non-convex optimization problem. However, this achievement comes with expensive computation when the variable size is high. In this thesis work we mostly deal with non-convex constrained optimization problems as the work involves finding of appropriate means and covariances of nonlinear membership functions, matrices with certain sign, vectors having certain angles with some arbitrary vector, etc. GA has been frequently used in this thesis as it is good at handling such constraints while minimizing the objective value.
Approximating The Quadratic Programming (QP) Problem
Published in Megh R Goyal, Sustainable Biological Systems for Agriculture, 2018
The quadratic programming (QP) problem is the problem of minimizing a quadratic function over linear constraints. The quadratic programming has applications in areas such as public policy, transportation, engineering, finance, economics, agriculture, marketing, and resource allocation. For more on applications we refers to Gupta,6 Horst et al.8, and McCarl et al.12 The quadratic problem can be classified as convex and nonconvex. There are many exact methods for solving the convex quadratic programming problem. These exact methods include simplex-based complementary pivoting, active set, interior point, gradient projection, and augmented Lagrangian methods.1, 2, 4, 11, 13, 14 Unlike the convex quadratic, the nonconvex form is very difficult to solve. Heuristics are normally used to approximate this difficult model in reasonable times.3, 10
Optimal Localization and Sizing of UPFC to Solve the Reactive Power Dispatch Problem Under Unbalanced Conditions
Published in IETE Journal of Research, 2020
Shilpa S. Shrawane Kapse, Manoj B. Daigavane, Prema M. Daigavane
Despite the fact that the research focus has been made towards the optimization algorithms [15,17–21], the practical constraints that reside in the distribution systems are getting increased. Recently, the unbalanced distribution systems are found to be reported in the literature [22] by adopting optimization algorithms [23–32]. However, quadratic programming has handled the RPD problem under such a crucial unbalanced environment. Though quadratic programming is known for its accuracy, it is computationally inefficient and incapable to handle the multi-objective environment. Moreover, the problem domain becomes complex through the introduction of other security and cost constraints such as voltage profile and installation cost.
A Comprehensive Review on Stochastic Optimal Power Flow Problems and Solution Methodologies
Published in IETE Technical Review, 2023
Ankur Maheshwari, Yog Raj Sood, Supriya Jaiswal
The conventional approaches for solving OPF problems rely on linear programming (LP) [13], mixed-integer linear programming (MILP) [14], nonlinear programming (NLP) [15], lambda iteration method [16], interior point (IP) Method [17], dynamic programming (DP) [18], quadratic programming (QP) [19], lagrangian relaxation (LR) method [20], and others. These approaches are widely acknowledged in the literature as effective ways to address the complex OPF problems in power systems. The LP is the simplest method for giving a linear objective function and constraints. Considering nonlinear objective functions and their associated constraints led to the conception of NLP, which is widely employed to solve the OPF problem. The quadratic objective function with linear constraints comes under quadratic programming. IP method is also frequently employed and may effortlessly manage inequality constraints. Despite several advantages, these conventional approaches have several drawbacks, including the fact that the LP method linearizes nonlinear objective functions and constraints. The possibility of being stuck at local optima is the most significant disadvantage IP method. The NLP technique can be implemented in a large-scale system; however, one of the limitations is that it does not consider all the system’s components. In the case of large-scale OPF problems, DP takes a significant amount of processing time and is afflicted by the curse of dimensionality. MILP suffers similar drawbacks, requiring significant computational time and memory for solving large-scale OPF problems. Despite giving a fast solution, the LR method suffers from numerical convergence and suboptimal quality problems.
MOS Amplifier Design Methodology for Optimum Performance
Published in IETE Journal of Research, 2020
Abir J. Mondal, Paromita Bhattacharjee, Pinaki Chakraborty, Bidyut K. Bhattacharyya
Typically, NLP is written as, subject to where x1, x2, … … , xn are decision variables. The objective function and constraint equations in NLP can include any mathematical function such as sine, cosine, logarithm, and variables raised to high powers or to fractional powers. They may have a differentiable or non-differentiable form. However, if the objective is a quadratic function and the constraint equations are linear, then the problem is separately known as quadratic programming optimization problem [16].