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.

Anti-interference beam pattern design based on second-order cone programming optimization

When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.

Improved design of reconfigurable frequency response masking filters based on second-order cone programming

In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.

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.

Robust Blind Separation for MIMO Systems against Channel Mismatch Using Second-Order Cone Programming

To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem.

Feasibility and Structural Feature on Monotone Second-Order Cone Linear Complementarity Problems in Hilbert Space

Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q?H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.

A VU-decomposition method for a second-order cone programming problem

A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS

New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.

Positive Solutions for a Class of Second-order m-point Boundary Value Problems

Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.

海水淡化厂与区域水-能耦合系统的协同调度

海水淡化厂具有能量密集、运行灵活的特点,是理想的电力需求响应资源。然而,现有关于淡化厂与电网协同运行的研究大多关注电网和淡化厂的一体化调度、无法适应双方自主决策的工程场景,对淡化厂运行约束的刻画也比较粗糙。该文研究反渗透淡化厂与区域水-能耦合系统(waterenergy nexus,WEN)的协同运行方法。首先,考虑淡化厂的生产流程、调节特性和运行约束,分别建立传统及新能源淡化厂的水-能管理模型;其次,在保障两类淡化厂和区域WEN自主决策和信息隐私的条件下,提出以双方调度计划互动为载体的“激励型”和“价格型”两种协同运行机制及调度模型,并提出基于二阶锥松弛和McCormick包络的求解方法。用算例验证所提协同运行机制、调度模型及求解方法的有效性。

基于净能力及二阶锥规划的分布式光储多场景协同优化策略

针对现有配电网中分布式光储调度模型存在资源协同不足、求解复杂等问题,提出了一种基于净能力及二阶锥规划的分布式光储多场景协同优化调度策略。通过引入储能接入配电网后的功率转移分布因子,提出一种基于系统净能力的储能最优选址计算方法;综合考虑储能的运行特性和分布式光伏的出力不确定性,建立以系统日综合成本和削峰填谷为目标的分布式光储多场景协同优化调度模型;利用二阶锥松弛和Big-M法对潮流约束、储能运行约束进行处理,将原规划模型转化为混合整数二阶锥规划问题。以IEEE 33节点系统和西北某实际系统为算例进行仿真分析,结果表明所提方法能在降低负荷峰谷差和日综合成本、平抑负荷波动的同时,显著提高对分布式光伏的消纳能力,验证了所提方法的有效性和可行性。

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.

交流配电网分布鲁棒优化模型及快速求解算法

针对鲁棒优化保守性大、求解困难的缺点,本文提出交流配电网两阶段分布鲁棒优化模型及其快速求解算法。该模型以开关操作成本、微型燃气轮机发电成本、网损成本及弃风弃光切负荷成本最小为目标函数,构建基于置信区间的两阶段分布鲁棒优化模型;然后以电压的平方和相角为独立变量,提出变量替换结合二阶锥变换的模型转换新方法,将原模型转换为易于求解的混合整数二阶锥规划模型。算例分析表明,本文所提模型克服了基于盒式不确定集的鲁棒优化模型保守大的缺点,提高了算法求解速度。

RSS和AOA融合的单站低空无线电辐射源定位算法

提出一种在低空场景下基于接收信号强度(Rcecived Signal Strength,RSS)与到达角度(Angle of Arrival,AOA)信息融合的单站无源定位算法。该算法采用单架无人机设备虚拟多站设备接收无线电辐射源信号,融合RSS估计的距离信息与AOA方向角信息,依据最小二乘准则(LS)构造算法的优化目标函数,采用凸松弛技术将目标函数等价为二阶锥规划(SOCP)问题并通过内点法求解。实验结果表明,该算法的定位精度在2 km范围内可达20 m,其定位性能优于单站无源定位算法,且由于采用单架无人机采集信号,其设备复杂度相较于多站无源定位较低。

基于二阶锥规划的配电网源-网-荷-储联合规划方法设计

随着高比例分布式光伏接入配电网,如何对线路进行规划与源-储定址定容成为无法避免的问题。提出了配电网源-网-荷-储双层联合扩展规划策略,上层以配电网系统网络年投资费用最小和网损惩罚费用最小为目标建立线路规划模型,实现对配电网线路走向的改进;下层针对源、荷的不确定性以配电网运行收益最大为目标建立配电网源-储定址定容模型,同时引入不确定性参数对源-荷不确定性集的范围进行约束。针对所建双层规划模型非线性、难求解问题,基于二阶锥松弛算法将上述非凸、非线性优化规划模型转换为二阶锥优化模型,进而获得全局最优解,以此得到分布式光伏以及储能的最佳接入位置和容量。仿真结果表明,该方法可有效降低配电网的规划成本,促进分布式电源的消纳。

计及压缩机运行域的动态最优电-气能流凸化算法

压缩机是电-气互联系统的关键元件,其运行工作点是否位于运行域内关系到系统的安全稳定运行,同时其模型非凸性大幅增加了最优电-气能流的求解难度。为此,该文在压缩机准确建模的基础上,针对电力和天然气系统迥异的传输特性,提出一种计及压缩机运行域的动态最优电-气能流凸化算法。首先,根据压缩机运行参数与状态变量间的映射关系,构建压缩机三维运行域模型,并利用超平面实现运行域的凸包络松弛。其次,考虑差异化传输特性建立动态最优电-气能流模型,实现模型的混合整数二阶锥凸重构,并提出一种基于动态线性化与紧缩凸包络的凸化算法。最后,算例验证所提模型的有效性,表明所提算法在计算精度和效率上均优于连续锥规划算法。

计及多层级配电网的分布式新能源最大消纳空间分解测算

分布式新能源以“点多面广”的特征并入各级配电网,电网呈现新能源多层级接入、一体化消纳的特征。为促进新能源的充分消纳与高效利用,提出了一种多层级配电网新能源最大消纳空间测算模型,并将分布式新能源最大消纳空间测算问题转换为各层级配电网新能源最大消纳空间测算子问题,实现了各层级配电网分布式新能源最大消纳空间的精确测算。首先,以多层级配电网新能源接入量最大为目标函数,基于Distflow潮流模型建立多层级配电网分布式新能源消纳空间测算模型;然后,针对模型非凸以及求解效率低等问题,基于二阶锥松弛将模型转化为混合整数二阶锥规划模型,采用交替方向乘子法(alternating direction method of multipliers,ADMM),将多层级配电网新能源消纳空间测算问题转化为各级配电网新能源最大消纳空间子问题,将消纳空间模型转化为多层级配电网分布式新能源最大消纳空间分解测算模型;最后,以IEEE 6、7、9、10、12、15测试系统为例,验证该方法的有效性。

基于分布式新能源与配网网络重构的降损技术

考虑分布式新能源出力随机性对调控策略执行效果的影响,研究了基于电压风险评估和主动重构的日前调度技术。基于光伏出力预测和负荷预测,以电压安全概率风险最小为目标,以开合联络开关为控制变量,应用二阶锥松弛过的Distflow潮流模型进行求解,获取电压安全概率风险最小的配网重构方案。通过对IEEE 33节点配网进行算例分析,仿真结果验证了所提基于电压风险评估与主动重构的日前降损策略的可行性。

交直流电力系统与供热系统联合经济调度

随着热电联产等技术的广泛应用,电力系统和供热系统耦合日益紧密,电热联合调度得到了广泛的关注,但现有电热联合调度忽略了热网供电来源的多样性,由此提出了交直流电力系统与供热系统联合经济调度方法。首先,建立交直流电力系统模型,并提出一种线性近似方法对电压源变换器模型所带来的强非线性进行处理;然后,以运行成本最低为目标,建立考虑热网热惯性的交直流电力系统与供热系统联合调度模型,该模型中供热系统通过热电联产机组和交流电锅炉与交流电网耦合,通过直流电锅炉与直流电网耦合;最后,通过算例仿真验证了所提方法的有效性并说明了在电热联合调度中考虑交直流电源的必要性。