Second-order Cone Programming Approach Research Articles

Distributed Slack-Bus Based DC Optimal Power Flow With Transmission Loss: A Second-Order Cone Programming Approach and Sufficient Conditions

Distributed Slack-Bus Based DC Optimal Power Flow With Transmission Loss: A Second-Order Cone Programming Approach and Sufficient Conditions

Efficient Day-Ahead Scheduling of PV-STATCOMs in Medium-Voltage Distribution Networks Using a Second-Order Cone Relaxation

This paper utilizes convex optimization to implement a day-ahead scheduling strategy for operating a photovoltaic distribution static compensator (PV-STATCOM) in medium-voltage distribution networks. The nonlinear non-convex programming model of the day-ahead scheduling strategy is transformed into a convex optimization model using the second-order cone programming approach in the complex domain. The main goal of efficiently operating PV-STATCOMs in distribution networks is to dynamically compensate for the active and reactive power generated by renewable energy resources such as photovoltaic plants. This is achieved by controlling power electronic converters, usually voltage source converters, to manage reactive power with lagging or leading power factors. Numerical simulations were conducted to analyze the effects of different power factors on the IEEE 33- and 69-bus systems. The simulations considered operations with a unity power factor (active power injection only), a zero power factor (reactive power injection only), and a variable power factor (active and reactive power injections). The results demonstrated the benefits of dynamic, active and reactive power compensation in reducing grid power losses, voltage profile deviations, and energy purchasing costs at the substation terminals. These simulations were conducted using the CVX tool and the Gurobi solver in the MATLAB programming environment.

Advanced Flexibility Support through DSO-Coordinated Participation of DER Aggregators in the Balancing Market

Future power systems with a high share of intermittent renewable energy sources (RES) in the energy portfolio will have an increasing need for active power balancing. The integration of controllable and more flexible distributed energy resources (DERs) at the distribution-grid level represents a new solution and a sustainable alternative to conventional generation units for providing balancing services to the transmission system operator (TSO). Considering that the extensive participation of DERs in ancillary services may lead to the violation of limits in the distribution network, the distribution system operator (DSO) needs to have a more active role in this process. In this paper, a framework is presented that allows the DSO, as the central coordinator of the aggregators, to participate in the balancing market (BM) as a balancing service provider (BSP). The developed mathematical model is based on the mixed-integer second-order cone programming (MISOCP) approach and allows for determination of the limits of active power flexibility at the point of the TSO–DSO connection, formation of the dependence of the price/quantity curve, and achievement of the optimal dispatch of each DER after clearing the balancing market. The simulation results are presented and verified on modified IEEE distribution networks.

The efficiency evaluation and influencing factor analysis of regional green innovation: a refined dynamic network slacks-based measure approach

PurposeThis study aims to propose a refined dynamic network slacks-based measure (DNSBM) to evaluate the efficiency of China's regional green innovation system which consists of basic research, applied research and commercialization stages and explore the influencing factors of the stage efficiency.Design/methodology/approachA two-step procedure is employed. The first step proposes an improved DNSBM model with flexible settings of stages' input or output efficiency and uses second order cone programming (SOCP) to solve the non-linear problem. In the second step, least absolute shrinkage and selection operator (LASSO) and Tobit models are used to explore the influencing factors of the stage efficiency. Global Dynamic Malmquist Productivity Index (GDMPI) and Dagum Gini coefficient decomposition method are introduced for further discussion of the productivity change and regional differences.FindingsOn average, Chinese provincial green innovation efficiency should be improved by 24.11% to become efficient. The commercialization stage outperforms the stages of basic research and applied research. Comparisons between the proposed model and input-oriented, output-oriented and non-oriented DNSBM models show that the proposed model is more advanced because it allows some stages to have output-oriented model characteristics while the other stages have input-oriented model characteristics. The examination of the influencing factors reveals that the three stages of the green innovation system have quite diverse influencing factors. Further discussion reveals that Chinese green innovation productivity has increased by 39.85%, which is driven mainly by technology progress, and the increasing tendency of regional differences between northern and southern China should be paid attention to.Originality/valueThis study proposes an improved dynamic three-stage slacks-based measure (SBM) model that allows calculating output efficiency in some stages and input efficiency in the other stages with the application of SOCP approach. In order to capture productivity change, this study develops a GDMPI based on the DNSBM model. In practice, the efficiency of regional green innovation in China and the factors that influence each stage are examined.

Simultaneous siting and sizing of Soft Open Points and the allocation of tie switches in active distribution network considering network reconfiguration

Soft Open Points (SOPs) are power electronic devices and emerging flexible interconnections. The active and reactive power flow flexible controllability of SOP facilitates to improve the performance characteristics of the networks. To evaluate the contribution of SOPs to operational characteristics improvement, instead of a fixed number and an optimized configuration of SOPs is necessary. In addition to optimal siting and sizing of SOPs in distribution networks, considering the smart switching capability of SOPs compared to conventional switching through tie switches is important. This issue affects the decision of simultaneous investment for these types of equipment. Existing studies have not considered the coordinated presence of SOPs and candidate tie switches in a planning scheme for allocating them simultaneously. Here, a stochastic scenario-based planning model is proposed to determine the optimal sites and sizes of SOPs and the allocation of tie switches simultaneously while obtaining the optimal operation strategy of these devices during the network reconfiguration process. The model is formulated using the second-order cone programming approach. The optimization problem is solved considering renewable power production scenarios and different loading conditions. Finally, the proposed model is conducted on the IEEE 33-bus and 69-bus systems, and the results are presented.

Optimal Control for Kinematic Bicycle Model With Continuous-Time Safety Guarantees: A Sequential Second-Order Cone Programming Approach

The optimal control problem for the kinematic bicycle model is considered where the trajectories are required to satisfy the safety constraints in the continuous-time sense. Based on the differential flatness property of the model, necessary and sufficient conditions in the flat space are provided to guarantee safety in the state space. The optimal control problem is relaxed to the problem of solving three second-order cone programs (SOCPs) sequentially, which find the safe path, the trajectory duration, and the speed profile, respectively. Solutions of the three SOCPs together provide a sub-optimal solution to the original optimal control problem. Simulation examples and comparisons with state-of-the-art optimal control solvers are presented to demonstrate the effectiveness of the proposed approach.

Haze emission efficiency assessment and governance for sustainable development based on an improved network data envelopment analysis method

Accurate evaluation of emission governance efficiency can build fundament to develop haze control strategy towards sustainable development. By features of the haze, we view the haze formation stage as the first sub-process and the haze control stage as the second sub-process. This paper proposes an additive aggregation network data envelopment analysis (DEA) model with undesirable intermediate measures and undesirable outputs, which have not been thoroughly studied in previous literature. We found the newly developed network DEA model was nonlinear and cannot be converted into a linear program, and then developed an improved second-order cone programming approach to solve this problem. After analyzing the data of haze control in China, we drew the following conclusions: Firstly, different weights of preference for two sub-process can lead to the variation in the overall efficiency. Under different weights of preference, although the efficiency of the haze formation has a very small change in some provinces, the efficiency of the haze control has a large change. Secondly, decision makers can achieve the adjust goal of reducing haze by adjusting their preferences on the information of the haze formation and haze control stages, which are helpful for policy making in haze control strategy and sustainable development.

Distributed Multi-Energy Operation of Coupled Electricity, Heating, and Natural Gas Networks

This article proposes a distributed multi-period multi-energy operational model for the multi-carrier energy system. In this model, energy hubs function as distributed decision-makers and feature the synergistic interactions of generation, delivery, and consumption of coupled electrical, heating, and natural gas energy networks. The multi-period multi-energy scheduling is a challenging optimization problem due to its strong couplings and inherent nonconvexities within the multi-energy networks. The original problem is thus reformulated as a mixed integer second-order cone programming (MISOCP) and subsequently solved with a sequential second-order cone programming (SOCP) approach to guarantee a satisfactory convergence performance. Furthermore, a fully-distributed consensus-based alternating direction method of multipliers (ADMM) approach with only neighboring information exchange required is developed to optimize the multi-energy flows while considering the local energy-autonomy of heterogeneous energy hubs. The proposed methodology is performed and benchmarked on a four-hub urban multi-energy system over a 24 hourly scheduling periods. Simulation results demonstrated the superiority of the proposed scheme in system operational economy and renewable energy utilization, and also verify the effectiveness of the proposed distributed approach.

Attitude-Constrained Time-Optimal Trajectory Planning for Rotorcrafts: Theory and Application to Visual Servoing

In this article, a novel real-time time-optimal trajectory planning (TOTP) approach is proposed for rotorcrafts under velocity constraints and complex nonconvex thrust, attitude input constraints. Different from existing works, the proposed method is the first real-time TOTP solution for rotorcrafts subject to velocity constraints and these nonconvex input constraints. The key insight is to transform the thrust and attitude constraints into the inequality constraints on the quadratic nonlinear function of the path parameter acceleration and the squared velocity, by exploiting the differential flatness characteristic of the rotorcraft. As a result, the constraints can be formulated as the problem of jointly solving analytical quadratic inequalities. On this basis, a path acceleration calculation algorithm is proposed to obtain the backward and forward acceleration profiles. In addition, by formulating the well-known field of view (FOV) constraints into the attitude constraints, the proposed framework can further guarantee the FOV constraint for visual servoing of rotorcrafts. Comparative experimental results are presented to show the superior performance of the proposed approach when compared with the second-order cone programming approach. In addition, some visual servoing experiments are conducted to demonstrate the capability of the proposed method to guarantee the FOV constraint.

A Risk-Averse Shelter Location and Evacuation Routing Assignment Problem in an Uncertain Environment.

Disasters such as hurricanes, earthquakes and floods continue to have devastating socioeconomic impacts and endanger millions of lives. Shelters are safe zones that protect victims from possible damage, and evacuation routes are the paths from disaster zones toward shelter areas. To enable the timely evacuation of disaster zones, decisions regarding shelter location and routing assignment (i.e., traffic assignment) should be considered simultaneously. In this work, we propose a risk-averse stochastic programming model with a chance constraint that takes into account the uncertainty in the demand of disaster sites while minimizing the total evacuation time. The total evacuation time reflects the efficacy of emergency management from a system optimal (SO) perspective. A conditional value-at-risk (CVaR) is incorporated into the objective function to account for risk measures in the presence of uncertain post-disaster demand. We resolve the non-linear travel time function of traffic flow by employing a second-order cone programming (SOCP) approach and linearizing the non-linear chance constraints into a new mixed-integer linear programming (MILP) reformulation so that the problem can be directly solved by state-of-the-art optimization solvers. We illustrate the application of our model using two case studies. The first case study is used to demonstrate the difference between a risk-neutral model and our proposed model. An extensive computational study provides practical insight into the proposed modeling approach using another case study concerning the Black Saturday bushfire in Australia.

Equilibrium of Interdependent Gas and Electricity Markets With Marginal Price Based Bilateral Energy Trading

The increasing interdependencies between natural gas systems and power systems create new business opportunities in coupled energy distribution markets. This paper studies the marginal price based bilateral energy trading on the equilibrium of coupled natural gas and electricity distribution markets. Convex relaxation is employed to solve a multiperiod optimal power flow problem, which is used to clear the electricity market. A successive second-order cone programming approach is utilized to solve a multiperiod optimal gas flow problem, which is used to clear the gas market. In addition, the line pack effect in the gas network is considered, which can offer storage capacity and provide extra operation flexibility for both networks. In both problems, locational marginal energy prices are recovered from the Lagrangian multipliers associated with nodal balancing equations. Furthermore, a best-response decomposition algorithm is developed to identify the equilibrium of the coupled energy markets with bilateral gas and electricity trading, which leverages the computational superiority of SOCPs. Cases studies on two test systems validate the proposed methodology.

Second-Order Cone Programming Approach to Design of Linkage Mechanisms With Arbitrarily Inclined Hinges

An optimization approach is presented for generating linkage mechanisms consisting of frame members with arbitrarily inclined hinges. A second-order cone programming (SOCP) problem is solved to obtain the locations and directions of hinges of an infinitesimal mechanism. It is shown that the primal and dual SOCP problems correspond to the plastic limit analysis problems based on the lower-bound and upper-bound theorems, respectively, with quadratic yield functions. Constraints on displacement components are added to the dual problem, if a desirable deformation is not obtained. A finite mechanism is generated by carrying out geometrically nonlinear analysis and, if necessary, adding hinges and removing members. Effectiveness of the proposed method is demonstrated through examples of two- and three-dimensional mechanisms.

Alternating direction method of multipliers for truss topology optimization with limited number of nodes: a cardinality-constrained second-order cone programming approach

This paper addresses the compliance minimization of a truss, where the number of available nodes is limited. It is shown that this optimization problem can be recast as a second-order cone programming with a cardinality constraint. We propose a simple heuristic based on the alternative direction method of multipliers. The efficiency of the proposed method is compared with a global optimization approach based on mixed-integer second-order cone programming. Numerical experiments demonstrate that the proposed method often finds a solution having a good objective value with small computational cost.

An efficient second-order cone programming approach for optimal selection in tree breeding

It is common in forest tree breeding that selection of populations must consider conservation of genetic diversity, while at the same time attempting to maximize response to selection. To optimize selection in these situations, the constraint on genetic diversity can be mathematically described with the numerator relationship matrix as a quadratic constraint. Pong-Wong and Woolliams formulated the optimal selection problem using semidefinite programming (SDP). Their SDP approach gave an accurate optimal value, but required rather long computation time. In this paper, we propose an second-order cone programming (SOCP) approach to reduce the heavy computation cost. First, we demonstrate that a simple SOCP formulation achieves the same numerical solution as the SDP approach. A simple SOCP formulation is, however, not much more efficient compared to the SDP approach, so we focused on the sparsity structure of the numerator relationship matrix, and we develop a more efficient SOCP formulation using Henderson’s algorithm. Numerical results show that the proposed formulation, which we call a compact SOCP, greatly reduced computation time. In a case study, an optimal selection problem that demanded 39,200 s under the SDP approach was solved in less than 2 s by the compact SOCP formulation. The proposed approach is now available as a part of the software package OPSEL.

Two-stage optimization method for power loss and voltage profile control in distribution systems with DGs and EVs using stochastic second-order cone programming

This paper introduces a stochastic second-order cone programming (SSCOP) approach to solve the distributed generation coordination problem considering the uncertainty of electric vehicle charging in distribution networks. To minimize the total power loss in the distribution system, the problem is formulated to coordinate the output power of distributed generations (DGs). Two stages are presented to solve the optimization problem: the first stage is to optimize the output power of distributed generators without electric vehicle charging in the distribution system, and the second stage is to optimize the output power of distributed generators according to the stochastic increased load due to the uncertainty of electric vehicle charging. The proposed approach is tested on 69-node and 118-node large-scale distribution systems. The simulated results demonstrate the feasibility and effectiveness of SSCOP.

Double regularization methods for robust feature selection and SVM classification via DC programming

In this work, two novel formulations for embedded feature selection are presented. A second-order cone programming approach for Support Vector Machines is extended by adding a second regularizer to encourage feature elimination. The one- and the zero-norm penalties are used in combination with the Tikhonov regularization under a robust setting designed to correctly classify instances, up to a predefined error rate, even for the worst data distribution. The use of the zero norm leads to a nonconvex formulation, which is solved by using Difference of Convex (DC) functions, extending DC programming to second-order cones. Experiments on high-dimensional microarray datasets were performed, and the best performance was obtained with our approaches compared with well-known feature selection methods for Support Vector Machines.

A note on truss topology optimization under self-weight load: mixed-integer second-order cone programming approach

The self-weight load is a typical design-dependent load in structural optimization. This paper presents a mixed-integer second-order cone programming approach to global optimization of truss topology under the self-weight load.

Diversity Integration in Hybrid-ARQ With Chase Combining Under Partial CSI

We consider a receiver design for a Hybrid Automatic-Repeat-reQuest (HARQ) system protected by polar codes against transmission errors. This integrated detection–decoding receiver targets a packet link for which channel state information during HARQ retransmission is unavailable at the receiver. Under such channel uncertainties, we propose a second-order cone programming (SOCP) approach for diversity combining without resorting to decision-directed channel estimation prone to error propagation. We formulate an integrated SOCP receiver by jointly exploiting the constraints from diversity channel models, subspace separation, and forward error correction codes. Unlike traditional turbo receiver algorithms that require iterative exchange of soft information between detector and decoder, our proposed SOCP receiver solves as a single-integrated convex optimization problem. This formulation is also versatile and extendable to a plurality of practical scenarios. We further investigate the means for enhancing the receiver performance and the HARQ throughput. Numerical results demonstrate the substantial performance benefits of the proposed joint SOCP receiver.

Computing exact $D$-optimal designs by mixed integer second-order cone programming

Let the design of an experiment be represented by an $s$-dimensional vector $\mathbf {w}$ of weights with nonnegative components. Let the quality of $\mathbf {w}$ for the estimation of the parameters of the statistical model be measured by the criterion of $D$-optimality, defined as the $m$th root of the determinant of the information matrix $M(\mathbf {w})=\sum_{i=1}^sw_iA_iA_i^T$, where $A_i,i=1,\ldots,s$ are known matrices with $m$ rows. In this paper, we show that the criterion of $D$-optimality is second-order cone representable. As a result, the method of second-order cone programming can be used to compute an approximate $D$-optimal design with any system of linear constraints on the vector of weights. More importantly, the proposed characterization allows us to compute an exact $D$-optimal design, which is possible thanks to high-quality branch-and-cut solvers specialized to solve mixed integer second-order cone programming problems. Our results extend to the case of the criterion of $D_K$-optimality, which measures the quality of $\mathbf {w}$ for the estimation of a linear parameter subsystem defined by a full-rank coefficient matrix $K$. We prove that some other widely used criteria are also second-order cone representable, for instance, the criteria of $A$-, $A_K$-, $G$- and $I$-optimality. We present several numerical examples demonstrating the efficiency and general applicability of the proposed method. We show that in many cases the mixed integer second-order cone programming approach allows us to find a provably optimal exact design, while the standard heuristics systematically miss the optimum.

Global optimization of trusses with constraints on number of different cross-sections: a mixed-integer second-order cone programming approach

In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented in this paper is a new modeling of the design constraints for obtaining the minimum compliance truss design in which only a limited number of different cross-section sizes are employed. The member cross-sectional areas are considered either discrete design variables that can take only predetermined values or continuous design variables. In both cases it is shown that the compliance minimization problem can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution of this optimization problem is then computed by using an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to show that the proposed approach is applicable to moderately large-scale problems.