Second-order Cone Programming Model Research Articles

Minimization of the distribution operating costs with D-STATCOMS: A mixed-integer conic model

This paper addresses the problem of determining the optimal location and operation of distribution static synchronous compensators (D-STATCOMs) in power distribution networks. Metaheuristic algorithms have been conventionally used to solve this mixed-integer nonlinear programming problem. In contrast, we propose a mixed-integer second-order cone programming (MI-SOCP) model that guarantees global optimum and fast convergence of the algorithms in optimization solvers. The model seeks to minimize the annual installation cost and the operating cost, subject to active and reactive power balance constraints, voltage regulation bounds, devices capabilities, and the number of D-STATCOMs available to be connected. The multiobjective nature of the problem is also analyzed and solved using the proposed MI-SOCP model. An extensive set of simulations on the IEEE-33 nodes test system demonstrate the advantages of this approach compared to conventional heuristic algorithms and with solutions given by algebraic modeling software.

Increasing RES Hosting Capacity in Distribution Networks Through Closed-Loop Reconfiguration and Volt/VAr Control

This article presents a novel mixed-integer second-order cone programming model to increase the photovoltaic (PV) hosting capacity and optimize the operation of distribution networks. The problem considers voltage and reactive (Volt/VAr) control through the optimal operation of capacitors banks, substations’ on-load tap changers, voltage regulators, and network reconfiguration with radial and closed-loop operation topologies. The proposed formulation considers voltage-dependent models for loads and capacitor banks. The objective function maximizes the PV hosting capacity of the network. Numerical experiments are carried out using the 33-node and the 85-node networks. Results demonstrate the effectiveness of the proposed formulation to increase the penetration of PV sources, especially when the closed-loop operation is allowed, together with network reconfiguration and Volt/VAr control.

A mixed-integer second-order cone model for optimal siting and sizing of dynamic reactive power compensators in distribution grids

The problem of the optimal placement and sizing of dynamic reactive power compensators in AC distribution networks is addressed in this paper from convex optimization. The exact mixed-integer nonlinear programming (MINLP) model is transformed into a mixed-integer second-order cone programming (MISOCP) model. The main advantage of the MISOCP formulation is the possibility of finding a global optimum with branch & cut combined with interior-point method due to the convex structure of the continuous part of the problem, i.e., the multi-period branch optimal power flow. The dynamic reactive power compensators are sized and dimensioned considering daily load curves and variable reactive power injections. Numerical validations are tested in the 33- and 69-bus test feeders using the CVX tool available for MATLAB with the MOSEK solver. These simulations demonstrate the effectiveness and robustness of the MISOCP approach when compared with the solution of the exact MINLP obtained in the GAMS software.

A fault recovery strategy of flexible interconnected distribution network with SOP flexible closed-loop operation

With the continuous exploration of the application value of flexible interconnected distribution network, Soft Open Point (SOP) as its core device, how to fully explore the self-healing control support capability of SOP and improve its power supply reliability becomes particularly important. Aiming at the problem of fault recovery of flexible interconnected distribution network with multiple AC power supply areas, firstly, the topology of flexible interconnection of distribution network and the fault recovery model of SOP are described. Secondly, the stochastic nature of wind power, photovoltaic output and load is considered, and then the chance-constrained programming is introduced to deal with. Then, aiming at the coordinated operation of flexible closed-loop network in multiple AC power supply areas, and introducing the constraint on the acting number of switches, a stochastic optimization model of flexible interconnected distribution network fault recovery is established, and then the model is transformed into a deterministic mixed integer second-order cone programming model, which can be solved by CPLEX solver. Finally, the proposed model has been tested on a modified hand-in-hand IEEE33 system with dual-terminal SOP, verifying that the strategy proposed in this paper can effectively solve the fault recovery problem of flexible interconnected distribution network with multiple AC power supply areas considering uncertainty, and showing that this strategy can maximize the self-healing capability of distribution system.

Information flow-based second-order cone programming model for big data using rough concept lattice

Information flow-based second-order cone programming model for big data using rough concept lattice

Cluster Partition-Based Zonal Voltage Control for Distribution Networks With High Penetrated PVs

With the high penetrated photovoltaics (PVs) accessing distribution networks (DNs) in the future, the overvoltage of distribution network will be more serious, and the voltage control will be more complex. To solve this problem, a cluster partition-based zonal voltage control method for DN is proposed in this study. First, a cluster partition method using a comprehensive performance index is proposed: in terms of DN structure, a global density quality function index is introduced to measure the coupling degree of nodes in clusters. In terms of cluster function, the inconsistency coefficient index is presented to reflect the PV output characteristics, and a node membership function index is presented to limit the scale of the cluster. Then, the DN cluster partition is carried out under the fast Newman (FN) algorithm. Second, a second-order cone programming (SOCP) model of voltage control is established to maximize the PV consumption in each cluster. To achieve the coordinated optimization of clusters, an iterative optimization strategy among clusters is proposed. Finally, the effectiveness and rationality of the proposed method are verified in a 10 kV actual feeder system in Zhejiang Province, China.

On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks

The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416kW and 145.397kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver.

Transmission Grid Resiliency Investment Optimization Model With SOCP Recovery Planning

In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model.

Resilience-Oriented Distributed Load Restoration Method for Integrated Power Distribution and Natural Gas Systems

This study proposes a distributed load restoration method to effectively model and solve the load restoration problem of integrated power distribution and natural gas systems (IDGSs) after faults for resilient operation. The IDGS load restoration problem is devised as a mixed-integer second-order cone programming (MISOCP) model to minimize the total load loss cost of IDGS. This model considers distribution network reconfiguration and the coupling effect between the power distribution system (PDS) and natural gas system (NGS). Moreover, a bidirectional gas flow model is used to offer more flexibility for load restoration when the NGS is faulty. By considering the independent management and information privacy of each energy subsystem, the proposed model is solved using an alternating direction method of multipliers (ADMM) algorithm in a distributed manner. Furthermore, an adaptive-ADMM algorithm is used for convergence acceleration. Finally, numerical studies are conducted to validate the proposed methods effectiveness.

Multi-objective Dynamic Reconfiguration for Urban Distribution Network Considering Multi-level Switching Modes

The increasing integration of photovoltaic generators (PVGs) and the uneven economic development in different regions may cause the unbalanced spatial-temporal distribution of load demands in an urban distribution network (UDN). This may lead to undesired consequences, including PVG curtailment, load shedding, and equipment inefficiency, etc. Global dynamic reconfiguration provides a promising method to solve those challenges. However, the power flow transfer capabilities for different kinds of switches are diverse, and the willingness of distribution system operators (DSOs) to select them is also different. In this paper, we formulate a multi-objective dynamic reconfiguration optimization model suitable for multi-level switching modes to minimize the operation cost, load imbalance, and the PVG curtailment. The multi-level switching includes feeder-level switching, transformer-level switching, and substation-level switching. A novel load balancing index is devised to quantify the global load balancing degree at different levels. Then, a stochastic programming model based on selected scenarios is established to address the uncertainties of PVGs and loads. Afterward, the fuzzy c-means (FCMs) clustering is applied to divide the time periods of reconfiguration. Further-more, the modified binary particle swarm optimization (BPSO) and Cplex solver are combined to solve the proposed mixed-in-teger second-order cone programming (MISOCP) model. Numerical results based on the 148-node and 297-node systems are obtained to validate the effectiveness of the proposed method.

Optimal Scheduling for Flexible Regional Integrated Energy System with Soft Open Point

The Regional Integrated Energy System (RIES) has brought new modes of development, utilization, conversion, storage of energy. The introduction of Soft Open Point (SOP) and the application of Power to Gas (P2G) technology will greatly deepen the coupling of the electricity-gas integrated energy system, improve the flexibility and safety of the operation of the power system, and bring a deal of benefits to the power system. On this background, an optimal dispatch model of RIES combined cold, heat, gas and electricity with SOP is proposed. Firstly, RIES architecture with SOP and P2G is designed and its mathematical model also is built. Secondly, on the basis of considering the optimal scheduling of combined cold, heat, gas and electricity, the optimal scheduling model for RIES was established. After that, the original model is transformed into a mixed-integer second-order cone programming model by using linearization and second-order cone relaxation techniques, and the CPLEX solver is invoked to solve the optimization problem. Finally, the modified IEEE 33-bus system is used to analyze the benefits of SOP, P2G technology and lithium bromide absorption chillers in reducing system network loss and cost, as well as improving the system’s ability to absorb wind and solar and operating safety.

An integrated integer programming model with a simulated annealing heuristic for the carrier vehicle traveling salesman problem

We investigate a carrier vehicle traveling salesman problem (CVTSP) to visit n-targets in Euclidean space. Each target is visited by a smaller vehicle (e.g., UAV) consecutively, launched from and landed to a carrier. The smaller vehicle and the carrier must synchronize during both launching and landing. We present a mixed-integer second-order cone programming model with TSP-like constraints to determine the best target visiting sequence and the associated launch and land coordinates. A simulated annealing algorithm is implemented to shorten the computational time. The computational experiments indicate the simulated annealing algorithm calculates good CVTSP solutions within a reasonable amount of time.

Analysis of Artistic Modeling of Opera Stage Clothing Based on Big Data Clustering Algorithm

In order to deal with the problem that the traditional stage costume artistry analysis method cannot correct the results of big data clustering, which leads to deviations in the extraction of costume artistry features, this paper proposes a clothing artistic modeling method based on big data clustering algorithm. The proposed method provides a database for big data clustering by constructing the attribute set of the big data feature sequence training set and, at the same time, constructing a second-order cone programming model to correct the big data. Aiming at the problem that traditional stage costume art analysis methods cannot correct the clustering results of big data. On this basis, the costume elements of the opera stage are segmented, initialized, and transformed into a binary function. Finally, using the convolutional neural network, combining the element segmentation results and the large data clustering space state vector, a feature extraction model of stage costume art is constructed. Experimental results show that the model has good convergence, short time-consuming, high accuracy, and ideal feature recognition capabilities.

Optimal Economic–Environmental Operation of BESS in AC Distribution Systems: A Convex Multi-Objective Formulation

This paper deals with the multi-objective operation of battery energy storage systems (BESS) in AC distribution systems using a convex reformulation. The objective functions are CO2 emissions, and the costs of the daily energy losses are considered. The conventional non-linear nonconvex branch multi-period optimal power flow model is reformulated with a second-order cone programming (SOCP) model, which ensures finding the global optimum for each point present in the Pareto front. The weighting factors methodology is used to convert the multi-objective model into a convex single-objective model, which allows for finding the optimal Pareto front using an iterative search. Two operational scenarios regarding BESS are considered: (i) a unity power factor operation and (ii) a variable power factor operation. The numerical results demonstrate that including the reactive power capabilities in BESS reduces 200 kg of CO2 emissions and USD 80 per day of operation. All of the numerical validations were developed in MATLAB 2020b with the CVX tool and the SEDUMI and SDPT3 solvers.

Spatial–temporal optimal dispatch of mobile energy storage for emergency power supply

Mobile energy storage (MES) is a typical flexible resource, which can be used to provide an emergency power supply for the distribution system. However, it is inevitable to consider the complicated coupling relations of mobile energy storage, transportation network, and power grid, which can cause issues of complex modeling and low efficiency. To address that, this paper proposes a mobile energy storage dispatch model to minimize the load curtailment. The framework of rolling optimization is established to update the optimal strategy with the real-time factors, including grid, transportation, and MES. To increase solving efficiency, the model is extended to a mixed integer second-order cone programming model. Finally, the simulation results demonstrate the effectiveness of the proposed method in various scenarios.

Economic dispatch for a regionally integrated heat and electricity system with variable pipeline flow direction

Traditional models of heating networks are not able to take into account the changes in the value and the direction of pipeline mass flow in a multi-heat-source district heating network or the time delay characteristics of the network with constant temperature and variable flow operation. A day-ahead dispatch model for regional integrated heating and electricity system based on improved second-order cone programming method is therefore proposed. We first construct a heating network transmission model with variable value and direction of pipeline mass flow, and then use a convex relaxation to transform this nonlinear model into a mixed-integer second-order cone programming model. A hydraulic time-delay correction model is then constructed to reflect the dynamic characteristics of the heating network under variable mass flow conditions. Finally, we establish a model of an electric boiler with thermal storage to improve the flexibility of the distribution network. Case studies are used to show that the optimised results are more economical in terms of both the variable value and direction of mass flow. The proposed programming method retains the variability in the flow direction and achieves precise relaxation without the need to solve for the initial value. We also verify that the hydraulic time delay characteristics have a strong influence on the optimised results of the regionally integrated heat–electricity system under conditions of constant temperature and variable flow. In addition, an electric boiler with thermal storage can reduce renewable energy curtailment and effectively improve operational flexibility.

A New Second-Order Cone Programming Model for Voltage Control of Power Distribution System With Inverter-Based Distributed Generation

In this article, a novel second-order cone programming based branch flow model is proposed for optimal power flow (OPF) in radial distribution networks. The main advantage of the proposed architecture is that it can recover the bus voltage angle difference and, thus, control the reactive power flow (PF), leading to a better voltage regulation in the network. Based on the line PF and the line impedance, a convex equation is derived and included with the model to retrieve the bus voltage angle difference. Finally, using the retrieved bus voltage angle difference within the global optimal solution space, an algorithm is developed to control the reactive flow for voltage regulation. The proposed model has been tested on modified IEEE 32 bus (IEEE 33 bus network) and IEEE 123 bus power network systems for different test cases. The simulation results are verified with the OpenDSS PF and the MatPower nonlinear programming (NLP) based OPF solutions. The computational efficiency of the proposed model is superior to the NLP models. Also, the proposed reactive flow control algorithm improves the voltage regulation of a network and promises a globally optimal solution.

Stochastic single allocation hub location problems with balanced utilization of hub capacities

This paper presents a stochastic formulation for capacitated single allocation hub location problems with uncertain demands, in which the balanced utilization of hub capacities is considered in the strategic decision making process. The demands are assumed to be independent random variables with known normal probability distributions. A stochastic programming model with joint chance constraints is established and then transformed into a second-order mixed-integer cone programming model. Furthermore, the proposed model is approximated by using piecewise tangent approximation and piecewise linear approximation techniques. For the approximated models, alternative reformulations are developed, and valid inequalities are employed to add to alternative reformulations. Extensive numerical experiments with CAB and AP data sets are conducted to evaluate the performance of the proposed methods, and analyze the configuration of hub-and-spoke networks and the utilization of hub capacities. Experimental results show that the optimal solution of proposed models can be obtained by using the two approximation techniques with a small number of tangent and linear segments. The developed alternative reformulations and valid inequalities can significantly improve computational efficiency. The entire unbalanced utilization degree of hub capacities can be greatly reduced with a small rise in the traditional operating cost.

Wind Farm Level Coordination for Optimal Inertial Control With a Second-Order Cone Predictive Model

Multiple wind farms (WFs) should be spatially and temporally coordinated during inertial control to avoid the under- or over-power supply. For this purpose, we propose a second-order cone predictive model to exploit the optimal inertial control scheme (ICS) of multiple WFs for under-frequency and over-frequency events. Specifically, we firstly build the nonlinear predictive model including the predictive models of synchronous generators and wind turbines (WTs), power flow model and the stable operating constraints. In this nonlinear model, multiple WFs can be properly coordinated to achieve the optimal ICS. Then, the approximation methods are proposed to recast the above nonlinear model as a second-order cone programming (SOCP), and a sequential SOCP algorithm (SSA) is presented for the optimal solution. The SOCP model is offline executed to generate the optimal power references of WFs, and power references are further fitted with 5-parameter piecewise curves to reduce the communication burden. Lastly, the fitted curves can be distributed to WF controllers to be online tracked after detecting the disturbance. Numerical tests are conducted based on the 5 WFs integrated IEEE 39-bus system to validate the effectiveness and superiority of the proposed method.

Distributed energy management for active distribution network considering aggregated office buildings

This paper proposes a distributed energy management for active distribution network (ADN) considering aggregated office buildings. It aims to dispatch the flexible resources of office buildings to actively participate in the optimization of the ADN. Firstly, by considering the comfortable indoor temperature range and travel habits of workers, an optimal operation model for the office building with integrated heating ventilation and air conditioning (HVAC) systems and electric vehicle (EV) charging piles is constructed. Secondly, based on the piecewise linearization and second-order cone relaxation (SOCR), an ADN optimization model with aggregated office buildings is formulated and converted into a mixed-integer second-order cone programming (MISOCP) model. Then, considering the private information protection, the alternating direction method of multipliers (ADMM) is used to solve the ADN optimization model to realize the distributed energy management of the ADN with aggregated office buildings. Finally, the scheduling results of the ADN optimization model under different comfortable indoor temperatures and control methods of EVs are analyzed in the winter heating scenario. Numerical results show that the proposed method can increase the penetration of distributed photovoltaic (PV) generation and decrease losses of the distribution network while ensuring the temperature and travel demands of workers in office buildings. The information privacy of each district can also be protected with the proposed method.