Convex Quadratic Programming Problem Research Articles

Network partition and distributed voltage coordination control strategy of active distribution network system considering photovoltaic uncertainty

Aiming at the voltage exceeding problem caused by the introduction of Photovoltaic (PV) in Active distribution network (ADN), a comprehensive electrical distance index was established considering active and reactive voltage sensitivity, and the uncertainty of traditional PV probability density function (PDF) was optimized by random simulation method. The electrical distance expectation matrix between nodes was established by discretization of PV output probability distribution characteristics, and the ADN system was partitioned by affinity propagation (AP) algorithm. Taking active power loss as the objective function, the non-convex reactive power optimization control problem is transformed into a convex quadratic programming problem by LinDistFlow equation. An improved alternating direction method of multipliers (ADMM) which adaptively adjusts the penalty parameters is used to convert the finite boundaries of adjacent regions into data. By coordinating on-load tap-changer (OLTC), capacitor banks (CBs), and PV inverters on different time scales, the fast optimal control of global voltage in ADN is realized. The proposed method is tested on IEEE 33-bus and IEEE 123-bus distribution systems. After the optimization control algorithm described in this paper, the system network loss was reduced by 3.88%. Compared with the semi-definite programming relaxation, the calculation speed of LinDistFlow equation is increased by 72.2%. The results fully verify the feasibility and high efficiency of the control strategy described in this paper.

Evaluation method of distributed photovoltaic maximum access capacity based on ADMM

With the increasing penetration rate of distributed photovoltaics in the distribution network, new requirements are put forward for the operation and control of distribution networks. In order to ensure that the distribution network can operate stably within a safe range, it is important to evaluate the maximum capacity of the distribution network that can be connected to distributed photovoltaics. Considering the high cost of centralized computing, high communication requirements, and poor reliability, it is difficult to adapt to the actual needs of the distribution network with large-scale access to distributed photovoltaics. Therefore, this paper proposes an ADMM-based distributed PV maximum access capacity evaluation method. This method takes the distributed photovoltaic access capacity and the active power loss of the distribution network line as the objective function and considers the power flow equation constraints, node voltage constraints, and line current carrying capacity constraints of the distribution network. By simplifying the model, the non-convex optimization problem is transformed into a convex quadratic programming problem, and the ADMM algorithm is used to solve the distributed solution to obtain the access strategy of distributed PV in various regions under different operating conditions. Finally, the IEEE-33 system is used as an example to simulate the calculation, and the experimental results verify the correctness and effectiveness of the method.

Anomaly Detection Method for Rocket Engines Based on Convex Optimized Information Fusion.

The power system, as a core component of a launch vehicle, has a crucial impact on the reliability and safety of a rocket launch. Due to the limited measurement information inside the engine, it is often challenging to realize fast and accurate anomaly detection. For this reason, this paper introduces the rocket flight state data to expand the information source for anomaly detection. However, engine measurement and rocket flight state information have different data distribution characteristics. To find the optimal data fusion scheme for anomaly detection, a data set information fusion algorithm based on convex optimization is proposed, which solves the optimal fusion parameter using the convex quadratic programming problem and then adopts the adaptive CUSUM algorithm to realize the fast and accurate anomaly detection of engine faults. Numerical simulation tests show that the algorithm proposed in this paper has a higher detection accuracy and lower detection time than the traditional algorithm.

Evaluation of Grid Support Capacity From Electrified Railways

High power level and temporal operation flexibility endow electric trains with great potential for improving grid resilience. It becomes crucial to quantify the grid support capacity (GSC) from large-scale electrified railways. This paper innovatively proposes a hierarchical train coordination and trajectory regulation method to evaluate and deliver the GSC from electrified railways. In the light of the mechanical energy consumption analysis of train running, the energy-oriented train operation model is proposed to avoid the nonlinear differential dynamics of train kinetics when coordinating large-scale trains. Then the aggregation and disaggregation of trains for grid support can be formulated as linear and convex quadratic programming problems respectively. To closely follow the reference power and enhance the feasibility of train operation, a novel iterative discretization approach is proposed to generate the precise reference trajectory. A sliding mode controller with disturbance bound adaption is devised to overcome the modeling errors and disturbances when deploying GSC in realistic environment. Comprehensive numerical examples verify the effectiveness of the proposed scheme, and demonstrate the significant grid support potential from collaborative electrified railways.

Numerical solution of box constrained separable convex quadratic programming problems

In this paper, minimization problems with a separable convex quadratic objective function subject to a linear equality constraint/linear equality constraints, and bounds on the variables (box constraints) are considered. A necessary and sufficient condition for a feasible solution to be an optimal solution to each of these problems has been established. A convergent polynomial algorithm for solving the problem with a linear equality constraint and bounded variables is proposed, and some numerical results, obtained by this algorithm, are presented.

Improved fuzzy sparse multi-class least squares support vector machine

The classification problem is a key area of research in machine learning. The Least Squares Support Vector Machine (LSSVM) is an important classifier that is commonly used to solve classification problems. Its widespread use stems from its replacement of the inequality constraint in the Support Vector Machine (SVM) with the equality constraint, which transforms the convex quadratic programming (QP) problem of SVM into the solution of linear equations. However, when dealing with multi-class classification problems, LSSVM faces the challenges of lack of sparsity and sample noises, which can negatively impact its performance. Based on the modeling characteristics and data distribution of the multi-class LSSVM model, this paper proposes two improvements and establishes an improved fuzzy sparse multi-class least squares support vector machine (IF-S-M-LSSVM). The first improvement adopts a non-iterative sparse algorithm, which can delete training sample points to different degrees by adjusting the sparse ratio. The second improvement addresses the impact of sample noise on determining the optimal hyperplane by adding a fuzzy membership degree based on sample density. The advantages of the new model, in terms of training speed and classification accuracy, are verified through UCI machine learning standard data set experiments. Finally, the statistical significance of the IF-S-M-LSSVM model is tested using the Friedman and Bonferroni-Dunn tests.

Estimating ensemble weights for bagging regressors based on the mean–variance portfolio framework

This paper presents a novel ensemble learning framework inspired by modern portfolio optimization to address regression problems. This formulation in the ensemble learning field allows determining the ensemble’s weights considering the error predictions of the base learners, the variability in their predictions, and the covariance among their predictions’ errors, which is completely aligned with the bias–variance–covariance theory. Under the framework proposed, four potential instantiations have also been provided. The first two ensemble models impose the non-negativity constraints on the ensemble’s weights (along with the equality constraint that the ensemble’s weights sum up to one) and are solved with the active set algorithm. The second two ensemble models do not include the non-negativity constraints on the ensemble’s weights (which in the financial literature are called the non-shorting constraints), giving rise to a convex quadratic programming (QP) problem (as the matrix included in the quadratic term is symmetric and positive definite) that is solved by the Lagrangian procedure. Extensive experiments with regression datasets evaluate the proposed ensemble framework. Comparisons with other state-of-the-art ensemble methods confirm that the ensemble framework yields the best overall performance.

Crosstalk tolerance analysis of coupled-line structures using least square-support vector machine technique

In this paper, crosstalk sensitivity analysis of a microwave coupled-line structure due to the fabrication imperfections is investigated using Least Square-Support Vector Machine (LS-SVM) method. Since LS-SVM uses a set of linear equations instead of a convex quadratic programming problem, the computational cost is extremely reduced compared to that of the well-known Monte Carlo (MC) analysis or even Support Vector Machine (SVM) without decreasing the accuracy. Using this method, the geometrical parameters of the coupled-line are assumed to be randomly distributed using the Latin Hypercube function and the variation range of each parameter is set to ± 50% around its central value. The frequency response of the coupled-line is estimated and compared with those of the measured and simulation ones for a few well-known practical case studies. The results show that the LS-SVM procedure quickly predicts the worst-case crosstalk expectation values and accurately anticipates the probability of obtaining various outcomes of the coupled-line for the specified parameter variation over a wide frequency range.

An efficient hierarchical electric vehicle charging control strategy

AbstractElectric vehicle (EV) has emerged as a crucial component in addressing both energy and environmental problems, and has become an essential part of nowadays' intelligent transportation systems. However, the charging demands of large amounts of EVs can put substantial pressure on power grid systems and cause potential grid congestion problems. In this article, we propose a hierarchical EV charging control strategy that considers the network‐wide communication overheads, computational complexity, total energy cost, EV user preferences, and data privacy protection. The hierarchical charging structure contains two phases, that is, a centralized control for EV aggregators and a distributed control for EVs within an aggregator. We prove that the centralized control with the objective to minimize the total energy cost of the power system constitutes a convex quadratic programming problem. Then a unique global optimum for the energy consumption profiles of EV aggregators can be achieved. The distributed charging control for EVs within an aggregator is studied using a generalized Nash equilibrium problem (GNEP). We show that the solution of the GNEP can be obtained via a variational inequality. Then the Solodov and Svaiter hyperplane projection method is employed to iteratively approach the variational equilibrium while ensuring the protection of EV users' data privacy. Extensive simulation studies are conducted to verify the correctness and effectiveness of our proposed hierarchical charging control algorithm for EVs.

Design of continuous-time recurrent neural networks with piecewise-linear activation function for generation of prescribed sequences of bipolar vectors

A recurrent neural network (RNN) can generate a sequence of patterns as the temporal evolution of the output vector. This paper focuses on a continuous-time RNN model with a piecewise-linear activation function that has neither external inputs nor hidden neurons, and studies the problem of finding the parameters of the model so that it generates a given sequence of bipolar vectors. First, a sufficient condition for the model to generate the desired sequence is derived, which is expressed as a system of linear inequalities in the parameters. Next, three approaches to finding solutions of the system of linear inequalities are proposed: One is formulated as a convex quadratic programming problem and others are linear programming problems. Then, two types of sequences of bipolar vectors that can be generated by the model are presented. Finally, the case where the model generates a periodic sequence of bipolar vectors is considered, and a sufficient condition for the trajectory of the state vector to converge to a limit cycle is provided.

An Improved DCC Model Based on Large-Dimensional Covariance Matrices Estimation and Its Applications

The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence of time-varying factor on the covariance matrix estimations. To remedy this, in this article, we propose an improved dynamic conditional correlation model (DCC) by using nonconvex optimization model under smoothly clipped absolute deviation and hard-threshold penalty functions. We first construct a nonconvex optimization model to obtain the optimal covariance matrix estimation, and then we use this covariance matrix estimation to replace the unconditional covariance matrix in the DCC model. The result shows that the loss of the proposed estimator is smaller than other variants of the DCC model in numerical experiments. Finally, we apply our proposed model to the classic Markowitz portfolio. The results show that the improved dynamic conditional correlation model performs better than the current DCC models.

An Offline Closed-Form Optimal Predictive Power Management Strategy for Plug-In Hybrid Electric Vehicles

This article develops an optimal predictive power management strategy (OP-PMS) for plug-in hybrid electric vehicles (PHEVs) to manage the remaining battery level throughout a defined journey. Apart from using the battery before charging it again at the destination, this approach also supports transit through an Ultra Low Emission Zone (ULEZ), where a PHEV needs to operate in pure electric mode to avoid emissions. This type of PHEV power management strategy (PMS) design problem is a noncausal control problem, where the power demand of the remaining driving cycle and the final battery energy level targets influence the current power management action. Rather than solving the whole optimization problem online, this article presents a simplification that leads to a closed-form analytic solution with parameters that can be computed offline. This article makes three key contributions. First, a novel input-linearization method is developed, which converts the OP-PMS into a convex quadratic programming (QP) problem that captures the essential model nonlinearities using an input transformation and a quadratic cost function. Second, the influence of future power demands and final targets on current energy management policy is explicitly quantified from a dynamic optimal control perspective. Third, the noncausal convex QP is approximated with a closed-form analytic solution that is calculated offline. This leads to a real-time implementable OP-PMS with coefficients that can be precalculated and stored in the engine control unit. To demonstrate the viability of this approach, numerical examples are provided based on a generic PHEV model to verify the efficacy of the proposed OP-PMS.

Data-driven risk-averse newsvendor problems: developing the CVaR criteria and support vector machines

Incorporating decision-makers' risk preferences into data-driven newsvendor models and developing machine learning methods to solve the models are the challenging problems addressed in this study. To consider different distributions and decision-makers' different risk preferences for the two losses of the total cost newsvendor model, the symmetrical, the partial symmetrical and the asymmetrical CVaR criteria are introduced. The regularisation, the primal-dual approach and the kernels in support vector machines are used to transform the data-driven risk-averse newsvendor problems under the CVaR criterion into the convex quadratic programming problems with good theoretical properties. Computational experiments are conducted on a real-world dataset. The models under the partial symmetrical and the asymmetrical CVaR criteria obtained good performances, but that under the symmetrical CVaR criterion suffered the underfitting problem. Two factors including the degrees of risk aversion for the two losses in the total cost newsvendor model and the empirical errors of data-driven models affect order decisions. The degrees of risk aversion for the two losses have anti-directional effects on order quantities. The introduction of asymmetrical CVaR criterion paves a new way to reveal the effects of different risk references for different losses on order decisions, and has the potential to improve newsvendor decisions.

Active input design for simultaneous fault estimation and fault-tolerant control of LPV systems

This paper considers the problem of integrating fault estimation (FE) and fault-tolerant control (FTC) for linear parameter varying (LPV) systems with inexact scheduling variables from a new perspective. Unlike the conventional passive FE approaches that maintain the performance of FE by only adjusting parametric matrices, the proposed method guarantees the precision and optimality of FE by actively designing optimal inputs at each time instant under the set-theoretic framework, which is named as active fault estimation (AFE). Meanwhile, by constructing a quadratic Lyapunov function, the stability of augmented estimation-error dynamics can be guaranteed based on H∞ setting by solving a group of matrix inequalities. In addition, the optimal inputs are also designed to implement the objective of integrated AFE and FTC for LPV systems, which leads to a balance between the goal of AFE and the reference output tracking performance. Although the original optimization problem computing the optimal inputs is not convex, it is proved that this problem can be equivalently transformed to a family of convex quadratic programming problems with linear constraints. At the end, a physical vehicle model is used to verify the effectiveness of our proposed integrated AFE and FTC method.

Coordinated voltage control for improved power system voltage stability by incorporating the reactive power reserve from wind farms

The absorption and output characteristics of reactive power of the doubly-fed induction generator (DFIG) greatly influence the voltage stability of PCC (Point of Common Coupling) where the wind farms are integrated into the bulk power grid. This study proposes a reactive power compensation strategy for coordinated voltage control (CVC) of PCC with large-scale wind farms to achieve the expected voltage quality of the power grid through a minimum amount of control actions in emergencies. To this end, the mechanism of reactive power and voltage control inside DFIG is first analyzed. Then, the concept of reactive power reserve (RPR) sensitivity concerning control actions is introduced and an index of voltage stability margin is proposed to evaluate and analyze the distance between the current operating point and the voltage collapse point by analyzing the relationship between reactive power reserve and voltage stability margin. In the event of an emergency, critical reactive power reserves are obtained to reduce the dimension and complexity of the control problem. The sensitivity of reactive power reserve and the control are formulated into a convex quadratic programming problem to optimize the control strategies for voltage stability. The proposed technology has been validated on the IEEE 39-bus system.

On the solution of quadratic programming problems

The problems of quadratic programming are examined in this paper, particularly, the convex quadratic programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions are formulated for the considered convex quadratic programming problems, and a necessary and sufficient condition for solvability and for optimal solution of this problem is stated and proved.

A Multi-Step Inertial Proximal Peaceman-Rachford Splitting Method for Separable Convex Programming

In this paper, we propose a multi-step inertial proximal Peaceman-Rachford splitting method (abbreviated as MIP-PRSM) for solving the two-block separable convex optimization problems with linear constraints, which is a unified framework for such Peaceman-Rachford splitting methods (PRSM)-based improved algorithms with inertial step. Furthermore, we establish the global convergence of the MIP-PRSM under some assumptions. Finally, some numerical experimental results on the least squares semidefinite programming (LSSP), LASSO, the convex quadratic programming problem (CQPP), total variation (TV) based denoising and medical image reconstruction problems demonstrate the efficiency of the proposed method.

A linearly convergent self-adaptive gradient projection algorithm for sparse signal reconstruction in compressive sensing

<abstract><p>For sparse signal reconstruction (SSR) problem in compressive sensing (CS), by the splitting technique, we first transform it into a continuously differentiable convex optimization problem, and then a new self-adaptive gradient projection algorithm is proposed to solve the SSR problem, which has fast solving speed and pinpoint accuracy when the dimension increases. Global convergence of the proposed algorithm is established in detail. Without any assumptions, we establish global $ R- $linear convergence rate of the proposed algorithm, which is a new result for constrained convex (rather than strictly convex) quadratic programming problem. Furthermore, we can also obtain an approximate optimal solution in a finite number of iterations. Some numerical experiments are made on the sparse signal recovery and image restoration to exhibit the efficiency of the proposed algorithm. Compared with the state-of-the-art algorithms in SSR problem, the proposed algorithm is more accurate and efficient.</p></abstract>

A Discrete-time Projection Neural Network for Solving Convex Quadratic Programming Problems with Hybrid Constraints

A Discrete-time Projection Neural Network for Solving Convex Quadratic Programming Problems with Hybrid Constraints

Ensemble Support Vector Recurrent Neural Network for Brain Signal Detection.

The brain-computer interface (BCI) P300 speller analyzes the P300 signals from the brain to achieve direct communication between humans and machines, which can assist patients with severe disabilities to control external machines or robots to complete expected tasks. Therefore, the classification method of P300 signals plays an important role in the development of BCI systems and technologies. In this article, a novel ensemble support vector recurrent neural network (E-SVRNN) framework is proposed and developed to acquire more accurate and efficient electroencephalogram (EEG) signal classification results. First, we construct a support vector machine (SVM) to formulate EEG signals recognizing model. Second, the SVM formulation is transformed into a standard convex quadratic programming (QP) problem. Third, the convex QP problem is solved by combining a varying parameter recurrent neural network (VPRNN) with a penalty function. Experimental results on BCI competition II and BCI competition III datasets demonstrate that the proposed E-SVRNN framework can achieve accuracy rates as high as 100% and 99%, respectively. In addition, the results of comparison experiments verify that the proposed E-SVRNN possesses the best recognition accuracy and information transfer rate (ITR) compared with most of the state-of-the-art algorithms.