A Novel PSO Algorithm for Optimal Production Cost of the Power Producers with Transient Stability Constraints

The application of a novel Particle Swarm Optimization (PSO) method called Fitness Distance Ratio PSO (FDR PSO) algorithm is described in this paper to determine the optimal power dispatch of the Independent Power Producers (IPP) with linear ramp model and transient stability constraints of the power producers. Generally the power producers must respond quickly to the changes in load and wheeling transactions. Moreover, it becomes necessary for the power producers to reschedule their power generation beyond their power limits to meet vulnerable situations like credible contingency and increase in load conditions. During this process, the ramping cost is incurred if they violate their permissible elastic limits. In this paper, optimal production costs of the power producers are computed with stepwise and piecewise linear ramp rate limits. Transient stability limits of the power producers are also considered as addi-tional rotor angle inequality constraints while solving the Optimal Power Flow (OPF) problem. The proposed algo-rithm is demonstrated on practical 10 bus and 26 bus systems and the results are compared with other optimization methods.

Voltage Stability Constrained Optimal Power Flow Using NSGA-II

Voltage stability has become an important issue in planning and operation of many power systems. This work includes multi-objective evolutionary algorithm techniques such as Genetic Algorithm (GA) and Non-dominated Sorting Genetic Algorithm II (NSGA II) approach for solving Voltage Stability Constrained-Optimal Power Flow (VSC-OPF). Base case generator power output, voltage magnitude of generator buses are taken as the control variables and maximum L-index of load buses is used to specify the voltage stability level of the system. Multi-Objective OPF, formulated as a multi-objective mixed integer nonlinear optimization problem, minimizes fuel cost and minimizes emission of gases, as well as improvement of voltage profile in the system. NSGA-II based OPF-case 1-Two objective-Min Fuel cost and Voltage stability index;case 2-Three objective-Min Fuel cost, Min Emission cost and Voltage stability index. The above method is tested on standard IEEE 30-bus test system and simulation results are done for base case and the two severe contingency cases and also on loaded conditions.

An Optimal DF Based Method for Transient Stability Analysis

The effect of energy on the natural environment has become increasingly severe as human consumption of fossil energy has increased.The capacity of the synchronous generators to keep working without losing synchronization when the system is exposed to severe faults such as short circuits is referred to as the power system’s transient stability.As the power system’s safe and stable operation and mechanism of action become more complicated,higher demands for accurate and rapid power system transient stability analysis are made.Current methods for analyzing transient stability are less accurate because they do not account formisclassification of unstable samples.As a result,this paper proposes a novel approach for analyzing transient stability.The key concept is to use deep forest(DF)and a neighborhood rough reduction approach together.Using the neighborhood rough sets,the original feature space is obtained by creating many optimal feature subsets at various granularity levels.Then,by deploying the DF cascade structure,the mapping connection between the transient stability state and the features is reinforced.The weighted voting technique is used in the learning process to increase the classification accuracy of unstable samples.When contrasted to current methods,simulation results indicate that the proposed approach outperforms them.

Small-signal Stability Constrained Optimal Power Flow Considering Eigenvalue Distribution

In the existing small-signal stability constrained optimal power flow(SSSC-OPF)algorithms,only the rightmost eigenvalue or eigenvalues that do not satisfy a given threshold,e.g.,damping ratio threshold and real-part threshold of eigenvalue,are considered in the small-signal stability constraints.The effect of steady-state,i.e.,operating point,changes on eigenvalues is not fully taken into account.In this paper,the small-signal stability constraint that can fully reflect the eigenvalue change and system dynamic performance requirement is formed by analyzing the eigenvalue distribution on the complex plane.The small-signal stability constraint is embedded into the standard optimal power flow model for generation reschedul-ing.The simultaneous solution formula of the SSSC-OPF is established and solved by the quasi-Newton approach,while penalty factors corresponding to the eigenvalue constraints are determined by the stabilization degree of constrained eigenvalues.To improve the computation speed,a hybrid algorithm for eigenvalue computation in the optimization process is proposed,which includes variable selection for eigenvalue estimation and strategy selection for eigenvalue computation.The effectiveness of the proposed algorithm is tested and validated on the New England 10-machine 39-bus system and a modified practical 68-machine 2395-bus system.

Solving Load Flow Problems of Power System by Explicit Pseudo-Transient Continuation (E-ψtc) Method

This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for example, the 11-bus system is not an ill-conditioned system. In addition, a new approach to solve Load Flow Problems, E-ψtc, is introduced. It is an explicit method;solving linear equations is not needed. It can handle very tough and very large systems. The advantage of this method has been fully proved by two examples. The authors give this new method a detailed description of how to use it to solve Load Flow Problems and successfully apply it to the 43-bus and the 11-bus systems. The authors also propose a strategy to test the reliability, and by solving gradient equations, this new method can answer if the solution exists or not.

Parallel computing of multi-contingency optimal power flow with transient stability constraints

To deal with the high dimensionality and computational density of the Optimal Power Flow model with Transient Stability Constraints(OTS),a credible criterion to determine transient stability is proposed based on swing curves of generator rotor and the characteristics of transient stability.With this method,the swing curves of all generator rotors will be independent one another.Therefore,when a parallel computing approach based on the MATLAB parallel toolbox is used to handle multi-contingency cases,the calculation speed is improved significantly.Finally,numerical simulations on three test systems including the NE-39 system,the IEEE 300-bus system,and 703-bus systems,show the effectiveness of the proposed method in reducing the computing time of OTS calculation.

Voltage Stability Constrained Optimal Power Flow for Unbalanced Distribution System Based on Semidefinite Programming

This paper proposes a voltage stability constrained optimal power flow(VSC-OPF)for an unbalanced distribution system with distributed generators(DGs)based on semidefinite programming(SDP).The AC optimal power flow(ACOPF)for unbalanced distribution systems is formulated as a chordal relaxation-based SDP model.The minimal singular value(MSV)of the power flow Jacobian matrix is adopted to indicate the voltage stability margin.The Jacobian matrix can be explicitly expressed by ACOPF state variables.The nonlinear constraint on the Jacobian MSV is then replaced with its maximal convex subset using linear matrix inequality(LMI),which can be incorporated in the SDP-based ACOPF formulation.A penalty technique is leveraged to improve the exactness of the SDP relaxation.Case studies performed on several IEEE test systems validate the effectiveness of the proposed method.

A Pragmatic Method to Determine Transient Stability Constrained with Interface Real Power Flow Limits via Power System Scenario Similarity

In practical power systems,operators generally keep interface flowing under the transient stability constrained with interface real power flow limits(TS-IRPFL)to guarantee transient stability of the system.Many methods of computing TS-IRPFL have been proposed.However,in practice,the method widely used to determine TS-IRPFL is based on selection and analysis of typical scenarios as well as scenario matching.First,typical scenarios are selected and analyzed to obtain accurate limits,then the scenario to be analyzed is matched with a certain typical scenario,whose limit is adopted as the forecast limit.In this paper,following the steps described above,a pragmatic method to determine TS-IRPFL is proposed.The proposed method utilizes data-driven tools to improve the steps of scenario selection and matching.First of all,we formulate a clear model of power system scenario similarity.Based on the similarity model,we develop a typical scenario selector by clustering and a scenario matcher by nearest neighbor algorithm.The proposed method is pragmatic because it does not change the existing procedure.Moreover,it is much more reasonable than the traditional method.Test results verify the validity of the method.

Two-stage Transient-stability-constrained Optimal Power Flow for Preventive Control of Rotor Angle Stability and Voltage Sags

In practice,an equilibrium point of the power system is considered transiently secure if it can withstand a specified contingency by maintaining transient evolution of rotor angles and voltage magnitudes within set bounds.A novel sequential approach is proposed to obtain transiently stable equilibrium points through the preventive control of transient stability and transient voltage sag(TVS)problems caused by a severe disturbance.The proposed approach conducts a sequence of non-heuristic optimal active power re-dispatch of the generators to steer the system toward a transiently secure operating point by sequentially solving the transient-stability-constrained optimal power flow(TSC-OPF)problems.In the proposed approach,there are two sequential projection stages,with the first stage ensuring the rotor angle stability and the second stage removing TVS in voltage magnitudes.In both projection stages,the projection operation corresponds to the TSC-OPF,with its formulation directly derived by adding only two steady-state variable-based transient constraints to the conventional OPF problem.The effectiveness of this approach is numerically demonstrated in terms of its accuracy and computational performance by using the Western System Coordinated Council(WSCC)3-machine 9-bus system and an equivalent model of the Mexican 46-machine 190-bus system.

Identification of the Worst-case Static Voltage Stability Margin Interval of AC/DC Power System Considering Uncertainty of Renewables

Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation output.This paper presents a bi-level optimal power flow(BLOPF)model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission lines.Constraints of uncertain load growth’s hypercone model and control mode switching of DC converter stations are considered in the BLOPF model.Moreover,uncertain RES output fluctuations are described as intervals,and two three-level optimal power flow(TLOPF)models are established to identify interval bounds of the system worst-case SVSM.The two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain variables.Then,transforming the inner level model into its dual form,max–min BLOPF models are simplified to single-level optimization models for direct solution.Calculation results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.

Theory and Method of Power System Integrated Security Region Irrelevant to Operation States:An Introduction

How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem.The computational burden of probabilistic security assessment is even more unimaginable.In order to solve such problems,a security region(SR)methodology is proposed,which is a brand-new methodology developed on the basis of the classical point-wise method.Tianjin University has been studying the SR methodology since the 1980s,and has achieved a series of original breakthroughs that are described in this paper.The integrated SR introduced in this paper is mainly defined in the power injection space,and includes SRs to ensure steady-state security,transient stability,static voltage stability,and smalldisturbance stability.These SRs are uniquely determined for a given network topology(as well as location and clearing process for transient faults)and given system component parameters,and are irrelevant to operation states.This paper presents 11 facts and related remarks to introduce the basic concepts,composition,dynamics nature,and topological and geometric characteristics of SRs.It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way.Thus,this article provides support for the systematic understanding,future research,and applications of SRs.The most critical finding on the topological and geometric characteristics of SRs is that,within the scope of engineering concern,the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes.Based on this finding,the calculation time for power system probabilistic security assessment(i.e.,risk analysis)and power system optimization with security constraints can be decreased by orders of magnitude.

Solvability identification and feasibility restoring of divergent optimal power flow problems

Optimal power flow (OPF) has been considered as an important problem in power systems. Although several excellent algorithms, such as Newton method and interior point method, have been developed to solve the OPF problem, divergences still often occur. Till now, few works have focused on the solv- ability identification and feasibility restoring of divergent OPF problems. In this paper, we propose a systematic approach to identify the solvability of divergent OPF problems, and restore a feasible solu- tion for unsolvable OPF cases. The proposed approach consists of two phases: solvability identifica- tion phase (SIP) and feasibility restoring phase (FRP). In SIP, a novel methodology based on problem transformation and active set is adopted to identify the solvability of divergent OPF problem. If a fea- sible solution can be obtained in SIP, then this divergent OPF problem is solvable, otherwise, FRP is used to restore a feasible or optimal solution by relaxing soft constraints and load shedding. In FRP, a feasibility restoring model is presented, and a priority-listing strategy of restoring actions is proposed to restore the unsolvable OPF problems. Numerical studies indicate that the proposed SIP and FRP are reliable to diagnose the solvability of the divergent OPF problems, give an index to measure the un- solvability, and restore an unsolvable OPF case.

区域新能源并网暂态功角稳定分析与紧急控制策略优化

随着新型电力系统发展和新能源机组不断投产,南方区域将形成多区域新能源与邻近常规电源联合集中接入系统的场景。新能源集中接入常与常规电源共用输电通道,将影响区域系统暂态稳定特性及输送通道的传输能力,使南方区域系统的安全稳定运行和风险防控面临了前所未有的挑战。为深入研究区域新能源送出的稳定特性建立了区域新能源交流集中送出的等值系统模型,分析了新能源并入对区域系统对暂态稳定特性影响的主要机理。基于等面积法则对区域送出系统暂态过程的加、减速面积进行了定量分析,提出了紧急控制切机策略的协调优化方法,实现区域送出传统机组与新能源机组紧急控制切机量及控制代价的最小化的切机策略配置。最终,基于广东区域海风火电打捆送出系统为例,对分析结果的正确性进行了验证。

计及不确定性的随机暂态稳定约束最优潮流

为应对电力系统中不确定性对系统安全稳定造成的显著影响,提出一种计及不确定性的随机暂态稳定约束最优潮流方法。首先,采用威布尔和正态分布分别描述风电和负荷两种不确定性变量。其次,设置相应的置信水平,基于机会约束理论建立相应的概率约束,以期望值形式表达目标函数,从而建立计及不确定性的随机暂态稳定约束最优潮流模型。然后,通过半不变量法和Gram-Charlier级数求取电力系统输出变量的累积分布函数,并利用改进量子粒子群算法进行求解。最后,算例分析验证了所提方法的优越性和有效性。

基于PCE的系统参数化暂态稳定约束最优潮流

为更好地应对电力系统中存在的不确定参数给暂态稳定性带来的影响,提出了一种基于多项式混沌展开(polynomial chaos expansion,PCE)和随机伽辽金法(stochastic Galerkin method,SGM)的参数化暂态稳定约束最优潮流(parameterized transient stability constrained optimal power flow,PTSCOPF)问题的求解方案。针对电力系统不确定参数建立PTSCOPF模型;基于PCE和SGM近似拟合参数化暂态稳定轨迹,将原始的微分代数方程组(differential algebraic equations,DAE)形式的PTSCOPF模型转化为代数方程组形式的参数化非线性规划(non-linear programming,NLP)问题;采用原始-对偶内点法求解该NLP问题。利用改进的新英格兰10机39节点系统算例进行了各项测试,仿真结果表明,所提方法能够实现系统在预想故障下保持暂态稳定的优化效果。

计及占空比限幅环节的直流配电系统暂态稳定性分析

大功率扰动条件下,限幅环节容易造成占空比出现饱和现象,直流配电系统就会由闭环控制退化成开环响应并出现暂态失稳。为此,文中开展了计及占空比限幅环节的直流配电系统暂态稳定性分析。首先,文中利用Sigmoid函数模拟占空比限幅环节中的非线性特性,建立了更为贴近工程实际的直流配电系统大信号模型。其次,利用Takagi-Sugeno(TS)模糊模型法,刻画了计及占空比限幅环节影响的估计吸引域。然后,通过不同控制参数的估计吸引域变化情况,揭示了占空比饱和引发的直流配电系统暂态失稳现象。最后,针对占空比限幅环节导致已有暂态稳定性提升方法存在的局限性,提出了一种控制参数优化设计的方法,为提升系统暂态稳定性的控制参数选择提供了方案。RT-Box硬件在环实验验证了理论分析的有效性。

融合关键机组信息与相平面图像的暂态稳定评估方法

针对传统基于电力系统时序数据的机器学习方法对系统深层耦合信息挖掘不充分的问题,将失稳模式作为先验知识引入机器学习,提出一种融合系统关键机组信息的暂态稳定性评估方法.该方法通过潮流追踪原理对线路计算各发电机潮流贡献度,得出系统关键机组权重.根据图像形态学原理,对相平面轨迹图像依照关键机组权重进行特征增强.在IEEE-39节点和IEEE-145节点系统下的仿真结果表明,所提方法较传统评估方法具有更好的评估性能,所构建的相平面图像样本较传统时序图像样本拥有更小的占用空间和更优的分类性能.

基于改进类电磁机制算法的UPFC多目标优化配置

统一潮流控制器(UPFC)能在不改变线路拓扑结构的条件下有效地改善电力系统潮流,从而提高输电能力与电压稳定性。针对系统可用输电能力、电压偏差和L指标等目标,建立了UPFC的多目标优化配置模型,采用结合差分进化算法(DE)的改进差分类电磁机制算法(DEEM)对所建模型进行求解,通过对算法中粒子的带电量、合力计算方式进行改进,同时添加自适应因子,进一步平衡算法的全局搜索与局部搜索能力。配置后的结果表明UPFC对增强系统输电能力、电压质量及电压稳定性的性能均有提高,且改进算法寻优效率的提升也得到了验证。

基于配点法的参数化暂态稳定性约束的电力最优潮流分析

为实现针对暂态稳定约束最优潮流的精确描述,提出一套参数化TSCOPF模型。通过该模型来判定电力系统中可变参数与TSCOPF解之间的定量关系。借助可变参数的多项式表达式来逼近参数化TSCOPF的最优解。在此基础上,只需在参数化TSCOPF中代入电力系统的可变参数即可取得符合暂态稳定性的最优控制方案。

A Data-driven Method for Transient Stability Margin Prediction Based on Security Region

Transient stability assessment(TSA)based on security region is of great significance to the security of power systems.In this paper,we propose a novel methodology for the assessment of online transient stability margin.Combined with a geographic information system(GIS)and transformation rules,the topology information and pre-fault power flow characteristics can be extracted by 2 D computer-vision-based power flow images(CVPFIs).Then,a convolutional neural network(CNN)-based comprehensive network is constructed to map the relationship between the steady-state power flow and the generator stability indices under the anticipated contingency set.The network consists of two components:the classification network classifies the input samples into the credibly stable/unstable and uncertain categories,and the prediction network is utilized to further predict the generator stability indices of the categorized samples,which improves the network ability to distinguish between the samples with similar characteristics.The proposed methodology can be used to quickly and quantitatively evaluate the transient stability margin of a power system,and the simulation results validate the effectiveness of the method.