Second-order Cone Programming Problem Research Articles

Linear-time quasi-static stability detection for modular self-reconfigurable robots

We address the problem of detecting potential instability in the planned motion of modular self-reconfigurable robots. Previous research primarily focused on determining the system’s unique physical state but overlooked the mutual compensation effects of connection constraints. We introduce a linear-time quasi-static stability detection method for modular self-reconfigurable robots. The internal connections, non-connected contacts, and environmental contacts are considered, and the problem is modeled as a second-order cone program problem, whose solving time linearly increases with the number of modules. We aim to determine the critical stable state of the system and that is achieved by finding the required minimum characteristic connection strength. By analyzing the critical stable state, we can assess the system’s stability and identify potential broken connection points. Furthermore, the internal stability margin is defined to evaluate the configuration’s stability level. The suspension and object manipulation configurations are first demonstrated in simulation to analyze the effectiveness of the proposed algorithm. Subsequently, a series of physical experiments based on FreeSN were carried out. The calculated stable motion ranges of manipulator configurations are highly consistent with the actual sampling boundaries. Moreover, the proposed algorithm successfully predicts stability and identifies broken connections in diverse configurations, encompassing quadruped and closed-chain configurations on both even and uneven terrains. The load experiment further demonstrates that the impacts from unmodeled factors and input errors under normal conditions can be on a small scale. By combining the proposed detection method and stability margin, we open the door to realizing real-time motion planning on modular self-reconfigurable robots.

Clutter-Sensing-Driven Space-Time Adaptive Processing Approach for Airborne Sub-Array-Level Digital Array

Sub-array-level digital arrays effectively diminish the computational complexity and sample demand of space-time adaptive processing (STAP), thus finding extensive applications in many airborne platforms. Nonetheless, airborne sub-array-level digital array radar still encounters pronounced performance deterioration in highly heterogeneous clutter environments due to inadequate training samples. To address this issue, a clutter-sensing-driven STAP approach for airborne sub-array-level digital arrays is proposed in this paper. Firstly, we derive a signal model of sub-array-level clutter sensing in detail and then further analyze the influence of the sidelobe characteristics of the conventional sub-array joint beam on clutter sensing. Secondly, a sub-array joint beam optimization model is proposed, which optimizes the sub-array joint beam into a wide beam with flat-top characteristics to improve the clutter-sensing performance in the beam sidelobe region. Finally, we decompose the complex optimization problem into two subproblems and then relax them into the low sidelobe-shaped beam pattern synthesisproblem and second-order cone programming problem, which can be effectively solved. The effectiveness of the proposed approach is validated in a real clutter environment through numerical experiments.

Modeling EV dynamic wireless charging loads and constructing risk constrained operating strategy for associated distribution systems

Dynamic wireless charging (DWC) is an emerging technology that enables the charging of electric vehicles (EVs) while they are in motion. However, previous load modeling methods have not thoroughly explored the detailed analysis of DWC load characteristics. Existing research only considers the single-node supply mode for dynamic wireless charging roads (DWCRs), and the assessment of operational risks arising from the uncertain DWC loads has not been addressed. This paper begins by conducting an equivalent circuit analysis of a typical EV DWC system with multiple segmented coils. We present a more accurate trapezoidal power model for a single EV. Subsequently, we model the aggregated EV DWC load, accounting for traffic flow and headway using Poisson and negative exponential distribution functions, respectively. In the operation process, we consider a multi-node supply mode for DWCRs. To address the inaccuracy of long-term predictions, we propose a rolling optimization model to coordinate DWC and renewables with heterogeneous uncertainties by introducing a risk metric to manage potential uncertain risks. The proposed optimization model is transformed into a mixed-integer second-order cone programming (MISOCP) problem after convex relaxation. Finally, we conduct case studies to validate the proposed methods.

Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets

Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the probability distribution of random variables is contingent upon the decision variables, and the ambiguity set is defined through parameterization involving the mean and a covariance matrix, which also depend on the decision variables. This dependency makes DRO difficult to solve directly; therefore, first, we demonstrate that under the condition of a full-space support set, the original problem can be reduced to a second-order cone programming (SOCP) problem. Subsequently, we solve this second-order cone programming problem using a projection differential equation approach. Compared with the traditional methods, the differential equation method offers advantages in providing continuous and smooth solutions, offering inherent stability analysis, and possessing a rich mathematical toolbox, which make the differential equation a powerful and versatile tool for addressing complex optimization challenges.

Stochastic Convex Cone Programming for Joint Optimal BESS Operation and Q-Placement in Net-Zero Microgrids

Microgrids have emerged as a pivotal solution in the quest for efficient, resilient, and sustainable energy systems. Comprising diverse distributed energy resources, microgrids present a compelling opportunity to revolutionize how we generate, store, and distribute electricity, while simultaneously reducing carbon footprints. This paper proposes an optimal battery energy storage system (BESS) management scheme, along with capacitor placement for reactive power (Q)-compensation, and scheduling for the purpose of a renewable-based microgrid’s loss minimization. The proposed model evaluates the impact of BESS management on energy efficiency and analyzes how optimal scheduling of BESS influences system losses. Furthermore, it investigates the coordinated planning and operation of active assets within the microgrid, such as controllable capacitor banks, in enhancing overall efficiency. The model is formulated as a mixed-integer second-order cone programming (MISOCP) problem which is solved for both deterministic and stochastic generation and consumption data. The proposed model is tested on a 21-bus microgrid comprising photovoltaic and hydropower energy resources, and the efficacy of the model is approved by several case studies. The simulation results show that the proposed method can reduce microgrid energy losses by approximately 12 percent using the deterministic approach and around 14 percent with the stochastic approach.

Pre-filters design for weighted sum rate maximization in multiuser time reversal downlink systems

In high-speed multiuser Time Reversal (TR) downlink systems, the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference. Moreover, maximizing the weighted sum rate in such systems is a critical objective, since the weighting factors represent the priority of different users in different applications. However, it faces significant challenges as it is an NP-hard and non-convex problem. In order to suppress these interferences and maximize the weighted sum rate, in this paper we present a novel approach for the joint design of the pre-filters. The proposed method applies successive convex approximation to transform the original problem into a Second-Order Cone Programming (SOCP) problem. Then, a low-complexity iterative algorithm is provided to effectively solve the resulting SOCP problem. According to the simulation results, the proposed method reaches a local optimum within a few iterations and demonstrates superior performance in terms of weighted sum rate compared to the current algorithm.

Convex Approach to Real-Time Multiphase Trajectory Optimization for Urban Air Mobility

Electric vertical takeoff and landing technology has emerged as a promising solution to alleviate ground transportation congestion. However, the limited capacity of onboard batteries enforces hard time constraints for vehicle operations in a complex urban environment. Therefore, a constrained, real-time trajectory optimization method is necessary to enable safe and energy-efficient vehicle flight. Unfortunately, most existing trajectory optimization methods suffer from low computational efficiency, unpredictable convergence processes, and strong dependence on a good initial trajectory. In this paper, we employ a successive convex programming approach to solve the multiphase minimum-energy-cost electric vertical takeoff and landing vehicle trajectory optimization problem for urban air mobility applications. The main contribution is the development and validation of two novel convexification methods that find approximate optimal solutions to the multiphase nonlinear trajectory optimization problem in real time by solving a sequence of convex subproblems. Specifically, the first method transforms the original nonlinear problem into a sequence of second-order cone programming problems through a convenient change of variables and lossless convexification, while the second approach achieves a similar goal without the need for control convexification. The resulting convex subproblems can be solved reliably in real time by advanced interior point methods. The proposed methods are demonstrated through numerical simulations of two different urban air mobility scenarios and compared with the solution obtained from GPOPS-II, a state-of-the-art general-purpose optimal control solver. Our proposed sequential convex programming methods can obtain near-optimal solutions with faster computational speed than GPOPS-II.

Chance constrained optimal power-water flow: An iterative algorithm assisted by deep neural networks

The optimal power-water flow (OPWF) is a fundamental tool for operating integrated power and water networks. To address uncertainties in renewable energy and load demands, researchers have used chance-constrained models to investigate OPWF under uncertainty. However, existing work has limitations, such as oversimplified network representations, intractable problem formulations, and high computational burdens. This paper presents a chance-constrained OPWF formulation that incorporates detailed network constraints and stochastic uncertainties from wind speeds and electricity/water demands. By leveraging the concept of quantiles of stochastic variables and convexification techniques, the model is recast into a deterministic mixed-integer second-order cone programming (MISOCP) problem with uncertain margins. To efficiently solve this problem, we propose a novel iterative algorithm assisted by deep neural networks (DNNs). The algorithm integrates two DNNs: one designed to solve power and water flow equations, accelerating the probabilistic evaluation of uncertain margins; and the other to predict pipeline flows and refine variable ranges, facilitating a warm-start approach to the MISOCP model. Case studies conducted on the IEEE 123-node feeder coupled with a 67-node water distribution network validate the two DNNs and the overall iterative algorithm. The findings demonstrate that the proposed DNN-assisted approach effectively balances system security and economy. Compared to existing algorithms, the relative error of the optimization solution is less than 0.03%, with a speedup ratio exceeding 200.

Fast Low-Sidelobe Pattern Synthesis Using the Symmetry of Array Geometry.

Array pattern synthesis with low sidelobe levels is widely used in practice. An effective way to incorporate sensor patterns in the design procedure is to use numerical optimization methods. However, the dimension of the optimization variables is very high for large-scale arrays, leading to high computational complexity. Fortunately, sensor arrays used in practice usually have symmetric structures that can be utilized to accelerate the optimization algorithms. This paper studies a fast pattern synthesis method by using the symmetry of array geometry. In this method, the problem of amplitude weighting is formulated as a second-order cone programming (SOCP) problem, in which the dynamic range of the weighting coefficients can also be taken into account. Then, by utilizing the symmetric property of array geometry, the dimension of the optimization problem as well as the number of constraints can be reduced significantly. As a consequence, the computational efficiency is greatly improved. Numerical experiments show that, for a uniform rectangular array (URA) with 1024 sensors, the computational efficiency is improved by a factor of 158, while for a uniform hexagonal array (UHA) with 1261 sensors, the improvement factor is 284.

Large deformation of cable networks with fiber sliding as a second-order cone programming

A new model for irreversible large deformations of fiber networks is developed. The fibers are considered as inextensible cables that slide relative to each other in the frictional junctions. This sliding is constituted by a rate-independent flow rule. The nonsmooth dissipation potential for each sliding system is defined as a product of the yield strength and the absolute value of the fiber sliding. The response of the cable segments is nonsmooth as well, since it shows asymmetry with respect to tension and compression. A principle of minimum incremental potential and a pure complementary energy principle are derived for the equilibrium incremental loading of the network at large deformations. They form a pair of primal and dual second-order cone programming problems with matching sets of displacement-based and force-based variables. These problems can be effectively solved by interior point methods that have many advantages compared to the gradient-based methods or dynamic relaxation. The model is extended by a simple mechanism of fiber pull-out resulting from fiber sliding at the free unconstrained ends. This can be used for the microstructural analysis of failure of needle-punched nonwoven materials.

A convex cone programming based implicit material point method

For conventional Material Point Method (MPM), both explicit-based and implicit-based MPM have shortcomings: explicit MPM has high requirements on time steps, and implicit MPM has high requirements on convergence. To circumvent these limitations, this paper innovatively proposes a convex cone programming-based implicit MPM (CP-MPM) algorithm, which ensures excellent convergence of solving complex problems involving large deformation, regardless of the chosen time step. In the proposed CP-MPM, the governing equations are initially transformed into a stationary point of a multivariable functional, leveraging the generalized Hellinger-Reissner (HR) variational principle. This stationary point problem is subsequently reformulated as a min-max convex cone optimization problem, with constraints originating from elastoplastic constitutive equations. In addition, a novel particle-based adhesive-frictional contact algorithm is proposed to effectively tackle the interaction between MPM domain and rigid bodies. The contact inequality between material points and rigid bodies is transformed into convex cone constraints, which rigorously prevent material point penetration and facilitate the imposition of irregular boundary conditions. Both elastic and elastoplastic problems involving contact under static or dynamic loading are ultimately represented as standard second-order cone programming (SOCP) problems, which is effectively solved by employing the Primal-Dual Interior Point (PDIP) method. The robustness, accuracy and convergence of the proposed method are validated through a series of elastic and elastoplastic benchmark problems. All results demonstrate the CP-MPM is a very promising method for implicitly solving complex practices.

Establishing a hierarchical local market structure using multi-cut Benders decomposition

Local electricity markets (LEMs) such as peer-to-peer (P2P) and community-based markets allow prosumers and consumers to exchange electricity products and services locally. In order to coordinate electricity trading and flexibility services, this paper proposes a hierarchical prosumer-centric market framework with a hybrid LEM and a local flexibility market (LFM). Multi-cut Benders decomposition (MCBD) is employed to decompose the integrated hybrid LEM into a centralized P2P market and multiple community-based markets. The aggregators coordinate energy sources and demands of households in low voltage (LV) distribution networks (DN) as virtual power plants (VPPs) and engage in trading through a P2P market over the medium voltage (MV) DN. In addition, a modified MCBD (M-MCBD) approach is proposed to accelerate the convergence process. The LFM is operated by the distribution system operator (DSO) and is formulated as a mixed-integer nonlinear programming (MINLP) problem which is further relaxed to a mixed-integer second-order cone programming (MI-SOCP) problem. The case study demonstrates that aggregators were able to collaborate on trading within the hybrid LEM to minimize the costs incurred by prosumers within the network. Furthermore, the proposed M-MCBD method improves the scalability of the MCBD by enhancing its convergence speed and accuracy, as demonstrated by testing on problems of varying scales.

Two-stage decision-dependent demand response driven by TCLs for distribution system resilience enhancement

Service restoration is a critical function of the self-healing distribution system to cope with extreme events. Cold load pickup (CLPU) caused by thermostatically controlled loads (TCLs) requires extra generation power to retore loads, slowing down the distribution system restoration process. Meanwhile, increasing renewable energy brings the supply-demand imbalance because of the power variability and may cause voltage or current violations. Accordingly, a two-stage decision-dependent demand response (DR) methodology is proposed to address the two barriers to distribution system resilience enhancement. Specifically, two load control strategies are developed in the first-stage DR to regulate TCLs for CLPU mitigation, which reduces the additional power requirement when re-energized. In the second-stage DR, the restored TCLs that can be controlled to provide flexibility are characterized as virtual energy storage (VES) for managing renewable energy variability. In this way, the required power generation is reduced, and the power fluctuation problem caused by renewable energy can be well addressed. It helps to speed up the load restoration and keep the distribution system operating securely. Moreover, the load profiles with CLPU mitigation control, VES parameters and VES availability time, depend on the re-energization time. In other words, load restoration decisions determine the two-stage DR. This is the most important finding of this paper and explicitly formulated in the load restoration model for accurate load characterization. The load restoration model is described by a mixed integer second-order cone programming (MISOCP) problem and solved using MATLAB 2021 with Gurobi solver. Case studies show that the proposed methodology can significantly mitigate CLPU and restore more loads. The decision-dependent behaviors of the two-stage DR are also validated.

A distributionally robust chance-constrained kernel-free quadratic surface support vector machine

This paper studies the problem of constructing a robust nonlinear classifier when the data set involves uncertainty and only the first- and second-order moments are known a priori. A distributionally robust chance-constrained kernel-free quadratic surface support vector machine (SVM) model is proposed using the moment information of the uncertain data. The proposed model is reformulated as a semidefinite programming problem and a second-order cone programming problem for efficient computations. A geometric interpretation of the proposed model is also provided. For commonly used data without prescribed uncertainty, a cluster-based data-driven approach is introduced to retrieve the hidden moment information that enables the proposed model for robust classification. Extensive computational experiments using synthetic and public benchmark data sets with or without uncertainty involved support the superior performance of the proposed model over other state-of-the-art SVM models, particularly when the data sets are massive and/or imbalanced.

A stable implicit nodal integration-based particle finite element method (N-PFEM) for modelling saturated soil dynamics

In this study, we present a novel nodal integration-based particle finite element method (N-PFEM) designed for the dynamic analysis of saturated soils. Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner (HR) variational principle, creating an implicit PFEM formulation. To mitigate the volumetric locking issue in low-order elements, we employ a node-based strain smoothing technique. By discretising field variables at the centre of smoothing cells, we achieve nodal integration over cells, eliminating the need for sophisticated mapping operations after re-meshing in the PFEM. We express the discretised governing equations as a min-max optimisation problem, which is further reformulated as a standard second-order cone programming (SOCP) problem. Stresses, pore water pressure, and displacements are simultaneously determined using the advanced primal-dual interior point method. Consequently, our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation. Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy, obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches. This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Carbon-Aware Operation of Resilient Vertical Farms in Active Distribution Networks

Emerging utilization of Electric Vehicles (EVs) in Distribution Networks (DNs) decreases the power quality in the DN. The main quest of this research is to find out Can EVs and Photovoltaic (PV) systems support the DN and mitigate the voltage magnitude violations due to utilizing high penetration level EV? This article proposes a novel volt/VAR optimization (VVO) model by leveraging the reactive power support of EVs and PVs as Distributed Energy Resources (DERs) for the DN. The proposed VVO model contains the second-order conic relaxed form of the AC power flow equations. Thus, the presented VVO problem is a Mixed-Integer Second-Order Cone Programming (MISOCP) problem. To obtain the ability to support the DN, Smart Inverters (SIs) are utilized to connect EVs and PV systems to the DN. Thus, to add the PV and EV systems to the convexified form of the VVO problem, the P-Q characteristics and the model of SIs working at different operating points are presented based on experimental results. The proposed model of SIs allows the participation of DERs in the reactive power compensation to mitigate voltage issues of DN due to utilizing high penetration level EVs. Besides, the proposed model of SIs enables DERs to increase their dispatchability. The performance of the proposed model is examined in the case studies using the IEEE 33-bus system and the 123-bus system. It is illustrated in the case studies that the solar dispatchability increases by 12% when the proposed volt/VAR model is utilized for IEEE 33-bus system. Besides, it is illustrated in the case studies that the voltage profile of buses remains in the desired operating range when the proposed model is leveraged, even if the penetration level of EVs increased to 40%.

Look-Ahead Rolling Economic Dispatch Approach for Wind-Thermal-Bundled Power System Considering Dynamic Ramping and Flexible Load Transfer Strategy

With a wind-thermal-bundled power system (WTBPS) under high wind penetration levels, the sharp power fluctuations of tie-lines for interconnected grids trigger a significant challenge of security-constrained power system operation. Smoothing power fluctuations with economic dispatch is widely concerned against this challenge. In this paper, an appropriate look-ahead economic dispatch framework for WTBPS considering the variable ramp rate of retrofitted coal-fired units and the flexible load transfer strategy (LTS) in high voltage distribution networks (HVDNs) is proposed. To cope with this issue, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) we derive a new family of tightened ramping constraints of retrofitted coal-fired units in the linear and second-order conic (SOC) forms, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) Using graph characterization of typical HVDNs, the simplified voltage-constrained LTS via topological structures can be developed. This proposed look-ahead economic dispatch model is cast as a mixed-integer second-order cone programming (MISOCP) problem, which can be reformulated by Multi-cut Generalized Benders Decomposition (MGBD). This MGBD enables multiple sub-problems can be solved in parallel and accelerates the solving process. Finally, simulation results of a large-scale practical system validate the computational accuracy and efficiency of the proposed approach.

A nonlinear relaxation-strategy-based algorithm for solving sum-of-linear-ratios problems

&lt;p&gt;This paper mainly studies the sum-of-linear-ratios problems, which have important applications in finance, economy and computational vision. In this process, we first propose a new method to re-represent the original problem as an equivalent problem (EP). Secondly, by relaxing these constraints, a nonlinear relaxation subproblem is constructed for EP. In view of the special structure of the relaxation, it is reconstructed as a second-order cone programming (SOCP) problem, which is essentially a SOCP relaxation of EP. Thirdly, through the structural characteristics of the objective function of EP, a region reduction technique is designed to accelerate the termination of the algorithm as much as possible. By integrating the SOCP relaxation and acceleration strategy into the branch and bound framework, a new global optimization algorithm is developed. Further, the theoretical convergence and computational complexity of the algorithm are analyzed. Numerical experiment results reveal that the algorithm is effective and feasible.&lt;/p&gt;

Stochastic model for active distribution networks planning: An analysis of the combination of active network management schemes

The widespread adoption of distributed generation (DG) is changing the operation of distribution networks. To increase the control of power flows and avoid the detriments of DG intermittency, active distribution networks (ADN) emerge as a feasible solution. In this paper, we propose a convex model for ADN expansion planning. Four active network management (ANM) schemes are considered: DG active power curtailment, DG reactive power control, on-load tap changer (OLTC) tap adjustment, and shunt compensation device control. The problem is formulated as a mixed integer second-order cone programming problem (MISOCP) using the distflow equations and second-order cone relaxations (SOCR). By scenario analysis, we address the uncertainty associated with power demand, renewable generation, and electricity prices. The proposed model is used to study the benefits of different combinations of ANM schemes to a modified IEEE 33-bus system and compare them with the individual benefits of each scheme. The results indicate that ANM schemes can reduce total network costs, reduce losses, delay network reinforcement, and improve the voltage profile. In addition, some combinations of schemes develop synergies in which the combined economic benefits are greater than the sum of the individual benefits.

Fault-Tolerant Controller Placement Model Considering Load-Dependent Sojourn Time in Software-Defined Network

This paper proposes a controller placement model that takes into account the load-dependent sojourn time at each controller while considering controller failures in a software-defined network. The sojourn time is expressed by the queuing theory. The sojourn time varies depending on the amount of load arriving at each controller in the proposed model. The proposed model is formulated as a mixed integer second-order cone programming (MISOCP) problem. The controller placement problem studied in this paper is proven to be NP-hard. We develop a heuristic algorithm for the case where the solution to an optimization problem of the proposed model cannot be obtained in practical time. The proposed model is compared with two baseline models presented in the previous research. In the baseline models, the sojourn time does not depend on the amount of load arriving at each controller. Numerical results show that the number of placed controllers becomes smaller in the proposed model than in the baseline models. We also compare results obtained by solving the MISOCP problem to those of the heuristic algorithm. Numerical results show that the heuristic algorithm reduces the computation time required to determine the controller placement, whereas the difference between the number of controllers determined by the heuristic algorithm and the optimal value is at most 4.84%. The number of controllers placed by the heuristic algorithm tends to decrease by considering network centrality.