Second-order Cone Programming Problem Research Articles

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.

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.

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.

Multi-objective adaptive trajectory optimization for industrial robot based on acceleration continuity constraint

In noncontact machining, such as welding and spraying, running efficiency and smoothness have been a bottleneck problem in trajectory optimisation of industrial robots. When the dynamic and mechanical properties of robots are fully utilised, significant impact are often produced. Thus, reducing the process impact of the robot and achieving a balance between the efficiency and smoothness of the operation process are complex problems that need to be solved. The trajectory optimisation problem is modelled based on the excellent properties of the convex-optimization (CO) problem. CO parameters were introduced to solve the inconsistency between the constrained and planned spaces. To obtain the weight factor of the multi-objective optimisation problem, a multi-objective adaptive optimisation method was proposed to select the optimal parameters. Aiming at the large process impact of the optimisation problem, which considers running time as the main optimisation objective, an acceleration continuity constraint method was proposed based on the smoothing path. Finally, the objective optimisation problem was transformed into a standardised second-order cone programming problem to complete the solution. The experimental results show that the proposed method can improve the robot operation efficiency and reduce the process impact by approximately 26% and 22%, respectively, from three aspects: optimum time, balance between efficiency and impact, and acceleration continuity.

The Cost and Benefit of Enhancing Cybersecurity for Hybrid AC/DC Grids

As critical interfaces of AC grids and DC grids inside a hybrid AC/DC grid, the voltage-sourced-converter (VSC) has been demonstrated to be vulnerable to false data injection (FDI) cyber-attacks. As a result, the cyber-attack-induced AC grid frequency deviations and DC grid voltage deviations threaten the secure operation. To enhance cybersecurity in a not only feasible but also cost-effective manner, this paper proposes a cost-benefit-based cyber-defense strategy for a hybrid AC/DC grid. First, this paper establishes a spatial-temporal dual cyber-attack evaluation model, in which the cyber-attack-induced frequency and voltage deviations are modelled in both a spatially and temporally dual manner. Then, the proposed cost-benefit-based cyber-defense strategy is modelled as a VSC commitment problem to achieve the trade-off between maximizing the cyber-defense benefits and minimizing the cyber-defense costs. The VSC commitment problem is then mathematically convexified into a mixed-integer second-order cone programming (MISOCP) problem, which could be efficiently solved in an event-triggered manner against unfolding cyber-attack events. Simulation results on a test hybrid AC/DC grid verified the feasibility and the cost-effectiveness of the proposed cyber-defense strategy.

Distributionally Robust Unit Commitment Considering Unimodality-Skewness Information of Wind Power Uncertainty

The deepening penetration of renewable energy sources (RESs) into power grids imposes remarkable challenges that merit special attention. In this paper, we work out a distributionally robust chance-constrained (DRCC) day-ahead unit commitment problem while the stochasticity and variability arising from RESs are taken into consideration. The developed framework optimizes the expected objective function and stipulates that the DRCCs will hold within a moment-based ambiguity set, which additionally incorporates the unimodality information and mode skewness. The employed ambiguity set can not only account for the wind power uncertainty but also expressly alleviate the conservatism compared with the single moment metric. By deriving efficient mathematical reformulations to tackle the expected objective function and DRCCs, the proposed model is reduced to an exact mixed-integer second-order cone programming problem that can readily be implemented. Numerical experiments are carried out on two representative test systems to demonstrate the effectiveness and efficiency of the suggested methodology.

Upper Bound Limit Analysis of 2D Structures Using Lagrange Extraction-Based Isogeometric Analysis

This work presents a new approach that uses Lagrange extraction-based isogeometric analysis and Second Order Cone Programming (SOCP) to determine the limit load factor in two-dimensional problems. This methodology makes use of an upper-bound limit approach and a rigid-perfectly plastic material model. Lagrange extraction is used to link a C0 nodal basis to a smooth B-spline basis. This enables the use of straightforward methods for isogeometric analysis in conventional finite element systems. A SOCP problem is created from the limit analysis problem, which may then be solved using Mosek optimization software. The numerical results indicate the correctness and effectiveness of the current technique by contrasting it with other approaches mentioned in the literature.

Optimal Dispatch of Battery Energy Storage in Distribution Network Considering Electrothermal-Aging Coupling

With the rapid development of distributed generation (DG), battery energy storage systems (BESSs) will play a critical role in supporting the high penetration of renewable DG in distribution networks. The traditional dispatching approach of BESSs commonly adopts linear models with constant operational characteristics and neglects the aging cost. However, the operational characteristics of BESSs are related to operational states, i.e., temperature, state of charge and current. Furthermore, the aging cost is also an important issue to optimize the economic profitability of BESSs, which is affected by the operational states as well. To this end, this paper proposes an optimal dispatch model of BESSs in distribution networks that considers the electrothermal-aging coupling relationship. The nonconvex original model is reformulated as a second-order cone programming problem, which can be effectively solved. Case studies show that the proposed method accurately captures the operational characteristics and synergistically optimizes the operational cost of distribution networks and the aging cost of BESSs. Compared to the traditional dispatching approach, the proposed method largely avoids the deviation between the scheduled power and actual power of BESSs and effectively saves the total cost, leading to a 48% extension of lifetime and a 30% increase in profitability of the BESSs.

Distributionally Robust Energy Management for Islanded Microgrids With Variable Moment Information: An MISOCP Approach

The ever-increasing penetration of renewable energy sources (RESs) has brought tremendous challenges to power system energy management problems. In this paper, we develop a distributionally robust (DR) joint chance-constrained microgrid energy management model while the uncertainties stemming from RESs are embedded. The proposed framework minimizes the expected cost function and ensures that the DR joint chance constraints (CCs) will satisfy for any distribution over a promising ambiguity set, which is designed based on the variable moments. The employed ambiguity set can describe the uncertainties more accurately compared with the commonly-used moment metric (i.e., fixed moments). By deriving equivalent second-order cone programming (SOCP) reformulations of the expected objective function and introducing effective approximation methods such as the optimized Bonferroni approximation to deal with the DR joint CCs, the proposed model is finally reduced to a tractable mixed-integer SOCP problem that can readily be solved. Case studies are conducted on a representative test system to corroborate the effectiveness of the suggested approach.

Network-Constrained Transactive Control for Multi-Microgrids-Based Distribution Networks With Soft Open Points

Different from most transactive control studies only focusing on economic aspect, this paper develops a novel network-constrained transactive control (NTC) framework that can address both economic and secure issues for a multi-microgrids-based distribution network considering uncertainties. In particular, we innovatively integrate a transactive energy market with the novel power-electronics device (i.e., soft open point) based AC power flow regulation technique to improve economic benefits for each individual microgrid and meanwhile ensure the voltage security of the entire distribution network. In this framework, a dynamic two-timescale NTC model consisting of slow-timescale pre-scheduling and real-time corrective scheduling stages is formulated to work against multiple system uncertainties. Moreover, the original bilevel game problems are transformed into a single-level mixed-integer second-order cone programming problem through KKT conditions, duality, linearization and relaxation techniques to avoid iterations of transitional methods, so as to improve the solving efficiency. Finally, numerical simulations on modified 33-bus and 123-bus test systems with multi-microgrids verify the effectiveness of the proposed framework.

部材の密集度を考慮した骨組構造物の大域的トポロジー最適化

It is known that the topology optimization (TopOpt) problem of frame structures can be formulated as a mixed-integer second-order cone programming problem (MISOCP), when the compliance is minimized and the cross-section of each member is selected from a set of predetermined candidates. However, when considering the constructability of real-world building structures, it is insufficient to only minimize compliance. In this paper, in order to control the density of members, the constraints of the number of members connected to each node are additionally considered into TopOpt by MISOCP treated in the previous study.

Nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic modelling of saturated soils under large deformation

This paper presents the nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic analysis of saturated soils subject to large deformation, utilising the generalised Hellinger-Reissner variational principle to reformulate the governing equations for saturated soil dynamics into a min–max optimisation problem. With finite element discretisation and nodal integration over cells, the problem is transformed into a standard second-order cone programming problem, efficiently resolved using the advanced primal–dual interior point method. The N-PFEM method has several advantages, including the use of linear triangular elements without volumetric locking issues, the avoidance of regularisation techniques, and the elimination of tedious variable mapping after remeshing. The numerical model is validated for large deformation analysis of saturated soils with a series of benchmarks against available analytical and numerical solutions, with a case study of the deformation of an embankment considering stone column reinforcement also carried out. This N-PFEM framework offers an effective and efficient simulation approach for the evolutionary behaviour of saturated soils with large deformation in complex geotechnical configurations of practical relevance.

Probabilistic wind power expansion planning of bundled wind-thermal generation system with retrofitted coal-fired plants using load transfer optimization

The bundled wind-thermal generation system (BWTGS) is an attractive option to integrate wind energy to actively participate in power systems. With the greatly enhanced penetration of wind energy in BWTGS, wind curtailment against sharp wind power fluctuations is inevitable. Thus, our study is stimulated by whether and to what extent we can maximize wind power penetration with proper provision of dispatchable loads against wind curtailment, and this is exactly the problem we aim to solve in this paper. Here, we initially focus on the flexible characteristics of retrofitted coal-fired units in BWTGS and the load transfer optimization (LTO) for high voltage distribution networks (HVDNs). Then, an appropriate probabilistic wind power capacity expansion planning method for BWTGS with retrofitted coal-fired units using LTO can be reformulated as a mixed-integer second-order cone programming problem. Moreover, since load and wind power data have inherited uncertainty, we extend this proposed model to be a probabilistic expanding model. This contributes to better decision-making for the short-term wind capacity expansion under quantified uncertainty. Numerical results of the practical HVDNs demonstrate the effectiveness of the proposed method.

Robust trajectory tracking and control allocation of X-rudder AUV with actuator uncertainty

This paper proposes a robust trajectory tracking control method for an X-rudder autonomous underwater vehicle subject to imprecise model parameters, unknown disturbances, and actuator uncertainty. The control scheme consists of a kinematics controller, dynamics controller, and rudder allocator constructed using backstepping techniques. The kinematics controller employs a line-of-sight guidance law, while the dynamics controller uses integral sliding mode and a Radial Basis Function Neural Network to handle modeling errors and unknown disturbances. Finally, a Recursive Least Square Control Allocation method is developed to minimize the allocation error considering the uncertainty in the control effectiveness matrix by solving a dual second-order cone programming problem. Simulation results demonstrate that the RBFNN-based trajectory tracking method achieves satisfactory performance in the presence of time-varying environmental disturbances, and the Recursive Least Square Control Allocation method effectively deals with actuator uncertainty.