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A piecewise linearization Based Method for Crossed Frequency Admittance Matrix Model Calculation of Harmonic Sources

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SENSORS 2025年第2期25卷 582-582页

作者： Yang, Youhang Wang, Shaorong Shi, Mingming Zheng, Xian Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan 430074 Peoples R China State Grid Jiangsu Elect Power Co Elect Power Res Inst Nanjing 211103 Peoples R China

The integration of large-scale power electronic equipment has intensified harmonic issues in power systems. Accurate harmonic models are fundamental for evaluating and mitigating harmonic problems, but existing models still exhibit deficiencies in harmonic mechanism, model complexity and accuracy. This work proposes a calculation method of crossed frequency admittance matrix (CFAM) analytical model based on piecewise linearization, aiming to achieve accurate modeling of phase-controlled power electronic harmonic sources. Firstly, the traditional CFAM model construction methods are introduced, and the shortcomings in harmonic modeling are discussed. Subsequently, the parameter-solving process of the CFAM analytical model based on piecewise linearization is proposed. This method improves the accuracy of harmonic modeling and simplifies the construction process of the analytical model. Furthermore, taking single-phase and three-phase bridge rectifiers as examples, CFAM analytical models under intermittent and continuous load current conditions are established, respectively, and the unified harmonic models for both conditions are summarized. Finally, case studies of rectifier harmonic sources under varying circuit control parameters and supply voltage distortions are conducted through Matlab/Simulink and experiments. The results demonstrate that the proposed method provides higher accuracy and more stable performance for harmonic current estimation compared with the traditional CFAM model and constant current source model.

关键词： power quality harmonic source model phase-controlled power electronic equipment piecewise linearization crossed frequency admittance matrix analytical model

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piecewise linearization of Quadratic Branch Flow Limits by Irregular Polygon

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第6期33卷 7301-7304页

作者： Pareek, Parikshil Verma, Ashu Indian Inst Technol Delhi Ctr Energy Studies New Delhi 110016 India

This letter addresses the issue of linearization of quadratic thermal limits of transmission lines for linear optimal power flow formulation. A new irregular polygon based linearization is proposed. The approach is purely based on geometrical concepts and does not introduce any optimization problem. Comparison of the number of constraints is given with different errors for different branch capabilities and systems. Test case analysis is also presented to validate the irregular polygon linearization strategy with optimal value and computational time results.

关键词： piecewise linearization linear optimal power flow (LOPF)

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Logarithm-transform piecewise linearization method for the optimization of fasoline blending processes

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Chinese Journal of Chemical Engineering 2018年第8期26卷 1684-1691页

作者： Yu Li Tong Qiu Department of Chemical Engineering Tsinghua University

Gasoline blending is a key process in a petroleum refinery, as it can yield 60%–70% of a typical refinery's total revenue. This process not only exhibits non-convex nonlinear blending behavior due to the complicated blend mechanism of various component feedstocks with different quality properties, but also involves global optimum searching among numerous blending recipes. Since blend products are required to meet a series of quality requirements and highly-sensitive to the proportion changes of blending feedstocks, global optimization methods for NLP problems are often difficult to be applied because of heavy computational burdens. Thus, piecewise linearization methods are naturally proposed to provide an approximate global optimum solution by adding binary variables into the models and converting the original NLP problems into MILP ones. In this paper, Logarithmtransform piecewise linearization(LTPL) method, an improved piecewise linearization, is proposed. In this method a logarithm transform is applied to convert multi-variable multi-degree constraints into a series of single-variable constraints. As a result, the number of 0–1 variables is greatly reduced. In the final part of this paper, an industrial case study is conducted to demonstrate the effectiveness of LTPL method. In principle, this method would be useful for blending problems with complicated empirical or theoretical models.

关键词： piecewise linearization Blending Non-convex Global optimization

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Real-time clothing insulation level classification based on model transfer learning and computer vision for PMV-based heating system optimization through piecewise linearization

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BUILDING AND ENVIRONMENT 2024年 253卷

作者： Wei, Zhichen Calautit, John Kaiser Wei, Shuangyu Tien, Paige Wenbin Univ Nottingham Dept Architecture & Built Environm Nottingham England

Achieving a balance between energy efficiency and thermal comfort is a key aspect of sustainable building design. Traditional control methods typically maintain indoor air temperature within predetermined limits, disregarding variable factors such as occupancy activity and clothing levels, which influence thermal comfort. Conversely, comfort-based control strategies present an opportunity to automate heating and cooling systems, enabling them to dynamically respond to variations in thermal comfort. To achieve this, real-time information on clothing insulation (and its adjustment) is indispensable for accurately estimating thermal comfort. In this study, we explore the potential of a novel detection approach capable of classifying clothing insulation in real-time and utilizing this information to optimize the operation of building energy systems. By doing so, the proposed method facilitates the delivery of indoor conditions tailored to user requirements and potentially reduces energy wastage. The development of a two-stage, computer vision-based framework for occupancy detection and clothing insulation classification forms the core of this approach. Leveraging deep learning algorithms, this framework performs detection and recognition tasks, even with limited training data effectively, enabling real-time classification of light, medium and heavy clothing. To address the nonlinearity of traditional predicted mean vote (PMV) models, we applied a piecewise linearization approach to our PMV-based optimal control strategy. We evaluated the performance of this detection method through initial experimental field tests conducted in a case study university building. The results demonstrate the proposed method's ability to classify clothing insulation levels and generate real-time profiles. We further analyze the impact of our proposed approach on thermal comfort and energy performance through scenario-based modelling and simulations. The initial results showed the potential o

关键词： Artificial intelligence Building energy Computer vision Clothing insulation Real -time comfort-based control Occupancy behaviour Predictive Mean Vote (PMV) Deep learning piecewise linearization Demand-driven heating ventilation and air conditioning (HVAC)

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Optimum Adaptive piecewise linearization: An Estimation Approach in Wind Power

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2017年第3期25卷 808-817页

作者： Vaezi, Masoud Khayyer, Pardis Izadian, Afshin Purdue Sch Engn & Technol Energy Syst & Power Elect Lab Indianapolis IN 46202 USA Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

This paper introduces an effective piecewise linearization technique to obtain an estimation of nonlinear models when their input-output domains include multidimensional operating points. The algorithm of a forward adaptive approach is introduced to identify the effective operating points for model linearization and adjust their domains for the maximum coverage and the minimum model linearization error. The technique obtains a minimum number of linearized models and the continuity of their domains. The algorithm also yields global minimum model linearization error. The introduced algorithm is formulated for a wind power transfer system for a 2-D set of input domains. The linearization error can be arbitrarily minimized in exchange for a higher number of models. The results demonstrate a significant improvement in the linearization of nonlinear models.

关键词： Adaptive continuity nonlinear hydraulic wind power piecewise linearization

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Correct the piecewise linearization Error of Quadratic Objective Function in DC OPF Model

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IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第6期34卷 5083-5086页

作者： Yang, Zhifang Lin, Wei Qiu, Feng Yu, Juan Yang, Gaofeng Chongqing Univ Dept Elect Engn Chongqing 400044 Peoples R China Argonne Natl Lab 9700 S Cass Ave Argonne IL 60439 USA State Grid Chongqing Elect Power Co Chongqing 400010 Peoples R China

In power industries and academia, piecewise linearization methods are widely used in optimal power flow (OPF) problems to approximate the nonlinear objective functions. Better computational performance can be achieved. However, limited attention has been paid to the approximation error. In electricity markets, this error could cause distortions of market clearing results and deficits in social welfare. To address this issue, we provide a criterion for the desired number of piecewise segments. We then propose an efficient method for correcting the piecewise linearization error of the DC OPF problems.

关键词： Karush-Kuhn-Tucker condition optimal power flow piecewise linearization electricity market

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A location-inventory supply chain problem: Reformulation and piecewise linearization

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COMPUTERS & INDUSTRIAL ENGINEERING 2015年 90卷 381-389页

作者： Diabat, Ali Theodorou, Effrosyni Masdar Inst Sci & Technol Dept Engn Syst & Management Abu Dhabi U Arab Emirates

In this paper, we study a two-echelon inventory management problem with multiple warehouses and retailers. The problem is a natural extension to the well-known one-warehouse multi-retailer inventory problem. The problem is formulated as a mixed integer non-linear program such that its continuous relaxation is non-convex. We propose an equivalent formulation with fewer non-linear terms in the objective function so that the continuous relaxation of the new model is a convex optimization problem. We use piecewise linearization to transform the resulting MINLP to a mixed integer program and we solve it using CPLEX. Through numerical experiments, we compare the solutions obtained by solving the new formulation using CPLEX with two previously published Lagrangian relaxation based heuristics to solve the original mixed integer non-linear program. We demonstrate that the new approach is capable of providing almost the same solutions without the need of using specialized algorithms. This important contribution further implies that additional variants of the problem, such as multiple products, capacitated warehouses and routing, can be added to result in a problem that will again be solvable by commercial optimization software, while the respective Lagrangian heuristics will fail to solve such variants or extended problems. (C) 2015 Published by Elsevier Ltd.

关键词： Supply chain Location-inventory Integer programming piecewise linearization

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A fast algorithm to compute the steady-state solution of nonlinear circuits by piecewise linearization

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COMPUTERS & ELECTRICAL ENGINEERING 2002年第2期28卷 91-101页

作者： Herdem, S Köksal, M Inonu Univ Fac Engn Dept Elect & Elect TR-44069 Malatya Turkey

In the last few decades, many types of nonlinear components that operate in switching modes have appeared in electrical and electronics engineering. These components are conveniently modeled by piece-wise linearization which results with linear circuits containing switches. Hence, the analysis of such circuits has gained more importance. In this paper, a fast algorithm for the steady-state solution of the nonlinear circuits of this type is considered. This algorithm implements maximum advantage when the lonlinearities are discrete and strong as in most of the power electronics semiconductor devices, (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： nonlinear circuits piecewise linearization switching equations control conditions

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An effective logarithmic formulation for piecewise linearization requiring no inequality constraint

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2021年第3期79卷 601-631页

作者： Hwang, F. J. Huang, Yao-Huei Univ Technol Sydney Sch Math & Phys Sci Transport Res Ctr Ultimo 2007 Australia Fu Jen Catholic Univ Dept Informat Management New Taipei 24205 Taiwan

One of the commonly used techniques for tackling the nonconvex optimization problems in which all the nonlinear terms are univariate is the piecewise linear approximation by which the nonlinear terms are reformulated. The performance of the linearization technique primarily depends on the quantities of variables and constraints required in the formulation of a piecewise linear function. The state-of-the-art linearization method introduces 2 [log(2) m] inequality constraints, where m is the number of line segments in the constructed piecewise linear function. This study proposes an effective alternative logarithmic scheme by which no inequality constraint is incurred. The price that more continuous variables are needed in the proposed scheme than in the state-of-the-art method is less than offset by the simultaneous inclusion of a system of equality constraints satisfying the canonical form and the absence of any inequality constraint. Our numerical experiments demonstrate that the developed scheme has the computational superiority, the degree of which increases with m.

关键词： Nonlinear programming Nonconvex optimization piecewise linearization Logarithmic method Inequality constraint

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Staircase compatibility and its applications in scheduling and piecewise linearization

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DISCRETE OPTIMIZATION 2018年 29卷 111-132页

作者： Baermann, Andreas Gellermann, Thorsten Merkert, Maximilian Schneider, Oskar Friedrich Alexander Univ Erlangen Nurnberg Lehrstuhl Wirtschaftsmath Dept Math Cauerstr 11 D-91058 Erlangen Germany

We introduce the Clique Problem with Multiple-Choice constraints (CPMC) and characterize a case where it is possible to give an efficient description of the convex hull of its feasible solutions. This special case, which we name staircase compatibility, generalizes common properties in several applications and allows for a linear description of the integer feasible solutions to (CPMC) with a totally unimodular constraint matrix of polynomial size. We derive two such totally unimodular reformulations for the problem: one that is obtained by a strengthening of the compatibility constraints and one that is based on a representation as a dual network flow problem. Furthermore, we show a natural way to derive integral solutions from fractional solutions to the problem by determining integral extreme points generating this fractional solution. We also evaluate our reformulations from a computational point of view by applying them to two different real-world problem settings. The first one is a problem in railway timetabling, where we try to adapt a given timetable slightly such that energy costs from operating the trains are reduced. The second one is the piecewise linearization of non-linear network flow problems, illustrated at the example of gas networks. In both cases, we are able to reduce the solution times significantly by passing to the theoretically stronger formulations of the problem. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Clique problem with multiple-choice constraints Staircase compatibility Total unimodularity Scheduling piecewise linearization

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