AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

Dispatchable Region for Active Distribution Networks Using Approximate Second-order Cone Relaxation

Uncertainty in distributed renewable generation threatens the security of power distribution systems.The concept of dispatchable region is developed to assess the ability of power systems to accommodate renewable generation at a given operating point.Although DC and linearized AC power flow equations are typically used to model dispatchable regions for transmission systems,these equations are rarely suitable for distribution networks.To achieve a suitable trade-off between accuracy and efficiency,this paper proposes a dispatchable region formulation for distribution networks using tight convex relaxation.Secondorder cone relaxation is adopted to reformulate AC power flow equations,which are then approximated by a polyhedron to improve tractability.Further,an efficient adaptive constraint generation algorithm is employed to construct the proposed dispatchable region.Case studies on distribution systems of various scales validate the computational efficiency and accuracy of the proposed method.

Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Lowner operator associated with a potential function for the optimization problems with inequality constraints.The favorable properties of both the Lowner operator and the corresponding augmented Lagrangian are discussed.And under some mild assumptions,the rate of convergence of the augmented Lagrange algorithm is studied in detail.

考虑智能软开关接入的主动配电网扩展规划方法

柔性互联装置的广泛应用给主动配电网(active distribution network,ADN)规划带来巨大挑战。该文提出一种考虑智能软开关(soft open point,SOP)接入的ADN扩展规划方法,对变电站新建及扩容,线路新建,智能软开关、分布式电源、储能系统以及无功补偿等设备的选址定容进行协同规划。首先,考虑分布式电源出力和负荷功率不确定性,采用基于改进高斯混合模型的聚类方法构建典型日场景。在此基础上,以年综合费用最小为目标函数,建立了考虑SOP接入的ADN扩展规划模型。然后,通过线性化和二阶锥松弛技术,将原始非凸非线性规划模型转化为混合整数二阶锥规划(mixed-integer second-order cone programming,MISOCP)模型,并提出逐次收缩凸松弛算法以获得凸松弛间隙足够小的原问题最优解。最后,在54节点主动配电网算例上验证了所提规划模型和求解算法的可行性与有效性。

改进二阶锥松弛和泰勒级数展开在TDOA无源定位中的应用

针对二阶锥松弛算法无法对凸包外的目标进行有效定位的问题,本文提出基于改进二阶锥松弛和泰勒级数展开的TDOA定位算法。首先,给出在视距条件下接收站位置信息无误差的TDOA定位的加权最小二乘模型;其次,简要分析凸包问题的形成原因,并提出解决思路,即在传统二阶锥松弛算法的基础上增加新的惩罚项,使松弛后的约束条件进一步逼近原问题约束,从而有效解决二阶锥松弛定位中的凸包问题。与此同时,文中还给出了新增惩罚项的选取准则;再次,将松弛后的模型转换成二阶锥形式进行求解;最后用二阶锥松弛算法的估计值作为初始值进行泰勒迭代,进一步提高估值精度。仿真结果表明本文算法有效,可以对凸包外的目标实现高精度定位,其RMSE曲线逼近克拉美罗下限。

基于交替方向乘子法的输-配-天然气系统分布式优化调度

随着电力网络与天然气网络耦合程度的加深以及传统配电网向主动配电网的转变,传统输配电气分离下的优化调度无法充分利用各种资源的灵活控制能力,不能获得整体最优解。因此,考虑电气耦合下的输配气协同优化,提出一种输-配-天然气系统优化调度模型。此外,考虑到未来输电系统运营中心、配电系统运营中心与天然气系统运营中心之间的独立性,为了保护各运营中心的信息隐私,提出了一个基于交替方向乘子法的分布式求解框架求解所提模型。为了确保分布式求解算法的收敛性,利用二阶锥松弛方法将气网优化问题转化为凸优化问题。算例结果表明,考虑电气耦合的输配气协同优化能够充分利用主动配电网中的多能耦合资源和储能资源,促进可再生能源消纳,提升系统总体运行经济性。此外,所提分布式求解算法的精确性和收敛性也得到了验证。

基于改进和声搜索算法与二阶锥松弛的储能优化配置

配电网中分布式电源的大量接入加剧了电网功率波动,为稳定电网功率及消纳新能源发电功率,需在电网中合理配置储能。基于双层规划模型将储能配置划分为规划层与运行层,并提出了基于趋向移动的全局和声搜索算法和二阶锥松弛理论相结合的储能优化配置混合算法。规划层采用以储能年投资成本与配电网年运行成本之和最小为目标函数,研究了储能配置位置、功率、容量等方面的经济效益;运行层以电网有功网损以及电压偏移之和最小为目标函数,研究了储能各时段最优充放电功率。基于某地实际数据,以33节点配电网为例进行了仿真分析,研究了不同场景下储能的配置方式以及探讨了本文混合算法的优异性。结果表明所提出的混合算法可以顺利求解该场景下的储能配置问题,证明了该混合算法有效性。同时,探讨了多场景下的储能配置方式,证明采用双层规划模型对储能进行配置有利于降低配电网综合成本。最后,将该混合算法与传统智能优化算法求解此类问题进行了比较分析,证明了该混合算法在求解此类问题上的快速性与准确性。

一种用于电-气互联系统运行优化的动态收缩凸松弛算法

提出了一种动态收缩凸松弛算法来解决电-气互联系统的运行优化问题。模型建立中,考虑了新能源与储能元件接入以及管存和气流方向等运行约束。所提算法利用了二阶锥松弛和凸包松弛的方法将非凸约束转换为凸约束,并通过动态收缩求解算法将电-气互联系统的运行优化问题转化为精确松弛域内的混合整数二阶规划问题加以求解。算例测试中,分别以修改的IEEE 39节点与IEEE 118节点电力系统和比利时20节点天然气系统组成的2个电-气互联系统为例,通过仿真验证了该算法有较佳的松弛精度和较快的计算速度。

计及机组有功与无功耦合特性的集群新能源电站无功优化

随着风电、光伏等新能源并网规模持续扩大和特高压直流等设备的接入,电力系统逐步呈现出高度电力电子化特征,为无功控制带来了新需求和新挑战。针对这一问题,首先介绍了双馈风机、直驱风机和光伏的动态无功调节能力模型,其次提出了考虑主动降有功的无功调节控制策略,并建立了新能源电站集群层面考虑有功的无功优化模型。然后采用二阶锥凸松弛算法和分段线性化算法相结合,提出了混合整数和二阶锥优化的求解方法,有效解决了模型的非线性非凸及混合整数规划求解的难题。最后基于某实际新能源集群并网系统进行仿真分析。仿真结果表明采用考虑主动降有功的无功调节控制策略能够显著提升系统的无功控制能力,改善电压控制效果,提高系统经济性,验证了所提模型的正确性和经济价值。

Convexification of Hybrid AC-DC Optimal Power Flow with Line-Commutated Converters

Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.

Application of Modified Progressive Hedging for Stochastic Unit Commitment in Electricity-Gas Coupled Systems

The increasing number of gas-fired units has significantly intensified the coupling between electric and gas power networks.Traditionally,nonlinearity and nonconvexity in gas flow equations,together with renewable-induced stochasticity,resulted in a computationally expensive model for unit commitment in electricity-gas coupled integrated energy systems(IES).To accelerate stochastic day-ahead scheduling,we applied and modified Progressive Hedging(PH),a heuristic approach that can be computed in parallel to yield scenario-independent unit commitment.Through early termination and enumeration techniques,the modified PH algorithm saves considerable com,putational time for certain generation cost settings or when the scale of the IES is large.Moreover,an adapted second-order cone relaxation(SOCR)is utilized to tackle the nonconvex gas flow equation.Case studies were performed on the IEEE 24.bus system/Belgium 20-node gas system and the IEEE 118-bus system/Belgium 20-node gas system.The computational efficiency when employing PH is 188 times that of commercial software,and the algorithm even outperforms Benders Decomposition.At the same time,the gap between the PH algorithm and the benchmark is less than 0.01% in both IES systems,which proves that the solutions produced by PH reach acceptable optimality in this stochastic UC problem.