An efficient method for optimal scheduling of fixed head hydro andthermal plants

An efficient and optimal method for scheduling thermal plants in coordination with fixed-head hydro units is presented. The method linearizes the coordination equation and solves for the water availability constraint separately from unit generation. Once the water constraint Lagrange multiplier is determined, the unit output can be computed easily. Case studies with various systems are presented and discussed     

考虑限幅约束的多区域互联电网全分布式潮流算法

多区域互联电网中有大量限幅非光滑约束,增加了潮流模型的非凸性。针对传统基于启发式规则处理限幅的分布式潮流算法在计算过程中容易出现收敛性问题,提出了一种能鲁棒性处理非光滑约束的互联电网全分布式潮流计算方法。首先根据分层分区调度模式对电网进行分区,并将模型中非光滑约束进行光滑处理,然后基于具有二阶收敛速度的双层交替方向非精确牛顿法,将潮流问题转化为求解最优步长增量的问题。基于零空间法(Null-Space)对状态变量的系数矩阵进行降维处理,采用共轭梯度(Conjugate Gradient, CG)算法更新每个分区的对偶乘子,乘子更新过程中利用二阶信息提高了算法的收敛性。多区域间进行分布式计算时无需协调层参与,仅需通信少量边界信息,因此通信负担轻。最后,以30节点和182节点系统为测试算例,验证了所提方法在设置恶劣初值和处理非光滑约束时具有较高的精确性和较好的收敛性。     

考虑风、水、燃气互济的中长期发电计划风险效益评估

发电企业的多种电源的协调安排能够达到企业运营效益的整体优化,而这种协调安排在市场条件下则更强调其风险和效益双重目标的实现。基于提高发电企业自主发电计划安排能力和实现企业增收避险的企业价值目标,该文对风、水、燃气三源互补发电的中长期发电计划进行了风险效益评估研究。首先,借助混合整数规划和随机规划理论,构建了发电计划中长期随机规划模型的目标函数,以及各机组运行约束,在其中重点构建了风-功、水-功转换约束;其次,基于双边合约市场和金融风险的市场规制条件,对发电企业的机组协调和风险规避策略进行了模型约束设计;再次,设计了基于拉格朗日乘数的模型算法流程和解决方案;最后,设计了3类电源机组的联合运营发电计划算例,利用蒙特卡洛设计情景模拟,实现了对不同发电安排的运营模拟和测算。算例验证了随机规划模型的可行性,该模型能够在不确定性环境和市场化条件下优化发电企业计划安排和机组协调能力,并能够帮助企业制定合理的收益预期并有效规避风险。     

一种新的分布式电力系统状态估计算法

随着电力系统的发展,区域电网互联,形成了规模更大的系统。为了适应这一趋势,电力系统状态估计应采用分布式算法。在配置少量PMU的基础上,将分区后的边界等式约束条件通过拉格朗日乘子计入整体目标函数,将分布式状态估计的问题转化为一个带等式约束的最优化问题,实现了电力系统状态估计的分布式计算。该算法不仅提高了状态估计的速度,而且可在不必改动原有状态估计模块的基础上,很容易地加入等式约束的修正模块。最后通过IEEE14节点和IEEE30节点系统的模拟仿真,验证了该算法的有效性和优越性。     

Short-Term Hydrothermal Power System Unit Commitment: A Comparative Study

To supply the required load, most electric power systems contain a combination of hydro and thermal power plants. The aim of this work is to study the optimal short-term operation of this combination, where the objective function is to minimize the thermal fuel cost and at the same time satisfy the hydro and thermal constraints, such as power balance at every hour, available water resources, reservoir volumes, and generation outputs limits. Two different techniques are used to solve the problem, namely dynamic programming and coordination equations. The mathematical algorithms for the solution of the problem were developed and the results of some computer studies on selected sample systems were obtained. The results show that using coordination equations method leads to lower total cumulative cost than using the dynamic programming method; however, many of the realistic system constraints cannot be properly handled by the coordination equations method.     

变质量高阶非完整系统具有未定乘子的两大类新型方程

本文在保留不独立坐标的情况下,用拉格朗日未定乘子法导出变质量高阶非完整系统的Appell方程及一类新型方程.     

计及中长期合同电量分解和风电不确定性的电-气综合能源系统日前优化调度

将中长期合同电量分解模型引入电-气综合能源系统日前调度决策过程中,实现了合同电量分解和调度计划制定的嵌套优化。针对合同电量分解结果可能在实际调度计划中不可执行的情况,提出了一种基于拉格朗日乘子的机组日分解电量越限因素定位方法,并通过中长期合同电量分解模型与日前调度模型的协调迭代消除越限电量,保证了中长期交易的有效性。此外,在模型中考虑了天然气网络约束和风电随机性对中长期交易计划的影响,并利用机会约束规划理论构建含风电不确定性的优化调度随机模型。基于风电等效随机输出样本矩阵和随机模拟技术实现机会约束向确定性表达式转化。通过仿真算例验证了所提方法的有效性。     

Advanced Coordination Method for Overcurrent Protection Relays Using Nonstandard Tripping Characteristics

This paper describes an advanced coordination method for an optimized protection time grading based on a new nonstandard tripping characteristic for overcurrent protection relays. The intention is the highest possible reduction of tripping times for a selective fault clearing in distribution networks protected by overcurrent relays without communication links. The new nonstandard tripping characteristic will be described from its basic idea to its constraints of the optimization problem. The optimization is solved by the method of Lagrange generalized with the Karush-Kuhn-Tucker conditions and is aimed at selective fault tripping with shorter tripping times as standard characteristics and conventional coordination methods. Overcurrent relay coordination becomes a mathematical optimization task. A comparison with the standard characteristics and conventional coordination methods shows a notable advancement regarding their average and maximum tripping times which can be achieved using this new method.     

MODELING THE INCREMENTAL COST AND WATER CONVERSION FUNCTIONS FOR HYDRO-THERMAL COORDINATION STUDIES

ABSTRACT

The solution of an optimization problem using variational means relies on Lagrange multiplier functions, called the adjoint variables to augment the physical constraints to the cost function. The multipliers usually have an economic interpretation, and in the optimal economic operation of an electric power system, one set of multipliers signifies the incremental cost of power delivered at a bus, and the other set relates to the water worth at a given reservoir. The solution of the optimization problem involves iterative techniques to obtain the optimal strategy in terms of power generations and water releases, as well as the adjoint variables. Good initial estimates are of paramount importance to a successful implementation of any iteration scheme specially those that are Newton based.

There is an observed pattern of dependence of the adjoint variables and the system state as described by power demands and water availability. Finding such relationships is useful for generation planning activities as well as in providing initial guesses in the numerical solution of the problem.

We propose statistical models for predicting the incremental cost function λ and the water conversion factor ν usually encountered in the hydro-thermal power system optimization problem. The method treats the active power demand and the volume of water available as the independent variables. The Least squares and the iteratively reweighted Least squares procedures are used to estimate model parameters. The approach treats the power system as a variable head hydro-thermal system, Kron's loss formula is used to characterize the system performance and losses. Results for an example using a 4 plant network are presented in order to demonstrate the applicability of this approach     

基于拉格朗日函数鞍距分配的广义内点法

不等式约束的处理是电力系统优化分析中比较困难的问题。文中根据拉格朗日函数的鞍点理论,将优化问题的等式约束进行松弛,形成计及等式约束的原始问题以及相应的对偶问题。通过定义原始和对偶问题之间的鞍距,并将鞍距在不等式约束之间进行分配,从而形成不同的针对不等式约束拉格朗日乘子的修正方程,进一步形成不同的优化算法。推导表明,内点罚函数法只是拉格朗日鞍点理论应用的一个特例。所提出的基于拉格朗日函数鞍距分配的广义内点法可以在电力系统优化分析中进行应用,将其应用于大规模间歇式电源接入情况下的电力系统最大传输能力问题中时,IEEE 30节点系统的计算结果及IEEE 14节点系统中不同算法的比较结果表明,此算法能够有效处理潮流问题不等式约束。     

系统分解协调算法的抽水蓄能电站优化调度

建立了包含抽水蓄能电站的电网统一调度优化模型,即以调度周期内火电燃料成本为最小目标函数,满足系统及各机组约束条件。利用系统分解协调思想,开发了一个结合拉格朗日松弛方法和粒子群优化算法的混合算法,将原优化问题分解为两层优化问题。上层拉格朗日算子优化利用次梯度算法求解,下层各子问题利用粒子群优化算法求解,经过迭代寻优得到最优对偶解后,利用一个启发式算法求得满足系统约束及各机组运行约束的原问题的可行解。最后通过算例验证了模型的合理性及算法的有效性。     

Observability analysis and bad data processing for state estimationwith equality constraints

A factorization-based observability analysis and the normalized residual-based bad-data processing have been carried out for state estimation using the normal equation approach. The observability analysis is conducted during the process of triangular factorization of the gain matrix. The normalized residuals are calculated using the sparse inverse of the gain matrix. The method of Lagrange multipliers is applied to handle state estimation with equality constraints arising from zero injections, because of its better numerical robustness. The method uses a different coefficient matrix in place of the gain matrix at each iteration. The factorization-based observability analysis and normalized residual-based bad-data processing are extended to state estimation with equality constraints. It is shown that the observability analysis can be carried out in the triangular factorization of the coefficient matrix, and the normalized residuals can be calculated using the sparse inverse of this matrix. Test results are presented     

计及统一潮流控制器的电力系统状态估计算法

在统一潮流控制器(UPFC)模型的基础上,提出了计及UPFC的电力系统状态估计算法。该算法根据给定的运行方式确定UPFC的控制约束条件,通过拉格朗日乘子将UPFC的控制约束条件计入状态估计目标函数,从而将含有UPFC的状态估计问题转化为带等式约束的最优化问题。该算法不仅可以完整地计及UPFC对电力系统的影响,而且可在不必改动原有状态估计模块的基础上,很容易地加入等式约束的修正模块。算例表明,提出的算法是有效可行的。     

Low‐complexity robust adaptive generalized sidelobe canceller detector for DS/CDMA systems

A novel low computational complexity robust adaptive blind multiuser detector, based on the minimum output energy (MOE) detector with multiple constraints and a quadratic inequality (QI) constraint is developed in this paper. Quadratic constraint has been a widespread approach to improve robustness against mismatch errors, uncertainties in estimating the data covariance matrix, and random perturbations in detector parameters. A diagonal loading technique is compulsory to achieve the quadratic constraint where the diagonal loading level is adjusted to satisfy the constrained value. Integrating the quadratic constraint into recursive algorithms seems to be a moot point since there is no closed‐form solution for the diagonal loading term. In this paper, the MOE detector of DS/CDMA system is implemented using a fast recursive steepest descent adaptive algorithm anchored in the generalized sidelobe canceller (GSC) structure with multiple constraints and a QI constraint on the adaptive portion of the GSC structure. The Lagrange multiplier method is exploited to solve the QI constraint. An optimal variable loading technique, which is capable of providing robustness against uncertainties and mismatch errors with low computational complexity is adopted. Simulations for several mismatch and random perturbations scenarios are conducted in a rich multipath environment with near–far effect to explore the robustness of the proposed detector. Copyright © 2008 John Wiley & Sons, Ltd.     

The minimization of voltage sag effect for specially connected transformers with a sensitive load and distributed generation systems

This paper improves the voltage sag for a distributed generation (DG) system with three-phase to two-phase connected transformers. The proposed connection system is compared with the systems designed by Scott and Le Blanc. A particle swarm optimization method with nonlinear time-varying evolution (PSO-NTVE) is used to determine the design values. This analysis considers sensitive loads and the coordination of over-current relays. The model uses a node admittance matrix for voltage sag calculation, in order to calculate the severity of system sag after single or two-phase faults. The analytical equations are useful in the mathematical optimal planning method. The PSO-NTVE is then used to derive suitable transformer impedances and relay time multiplier parameter values. The search for a global optimal solution for the voltage sag problems involves tests on the Scott and Le Blanc connected transformer power systems, in order to verify the effectiveness of the proposed method. Finally, the results show that the severity of the voltage sag is reduced by tuning the transformer impedances and relay settings.     

考虑负荷电压静特性的最佳乘子牛顿潮流算法

当考虑负荷电压静特性时，潮流方程不再为状态变量的二次函数，传统的求解病态潮流问题的最佳乘子牛顿法无法实施，该文提出了考虑负荷电压静特性的最佳乘子牛顿潮流算法。通过引入附加的状态变量并补充相应的潮流方程，使考虑负荷电压静特性后的直角坐标潮流方程仍保持为状态变量的二次函数，进而可以用最佳乘子牛顿法求解病态潮流问题。使用该方法能够保证潮流计算不发散，并且最佳乘子的求取同样简单，无近似，可以很容易地嵌入到常规的牛顿法潮流程序中，典型系统的数值试验结果表明了所提方法的正确性和有效性。     

考虑杠杆坏数据的参数辨识和快速修正方法

当存在杠杆坏数据时,现有的参数估计方法精度低、计算复杂,因此,该文提出一种基于拉格朗日乘子法的电网参数辨识和快速修正新方法。首先,建立了基于指数型目标函数的抗差状态估计模型,根据量测的误差大小而自动改变其权重,从而克服大部分坏数据,特别是杠杆坏数据对参数辨识精度的影响;进而基于拉格朗日乘子法确定可疑参数,再基于可疑参数在多个断面下的乘子值计算其用于误差修正的平均乘子值,实现参数误差的快速修正,并减少了计算量。通过3节点简单网络及IEEE 39系统的算例仿真,对比存在杠杆坏数据情况下该方法与传统方法的参数估计精度和计算时间,验证了所提方法的有效性和正确性。     

带界约束的仿射尺度信赖域法的无功优化

为有效处理无功优化模型中不等式约束且不扩大问题的规模,建立了与无功优化问题的库恩-塔克(KKT)条件等价的新模型。通过引入对角矩阵,消去KKT系统中关于界约束的互补关系,减少了变量维数,并采用一类求解带界约束非线性方程组的仿射尺度信赖域算法。该算法具有信赖域的全局搜索性和牛顿法的超线性收敛性,并可保持无功界约束的可行性。对IEEE-30、57、118节点系统进行仿真计算,并与常规非线性优化方法比较,结果表明该方法具有较好的收敛特性和计算效果。     

梯级电站等微增率方程组的分解协调算法

本文中，对电力系统经济调度中梯级电站的水系耦合，提出一种等微增率方程中也计及水系耦合影响，可利用稀疏矩阵技巧、又具有分解协调作用的算法，并提出了梯级电站经济运行的算例。算例计算结果表明，本文算法的收敛性，计算速度和计算结果的准确度均令人满意。     

基于简单排序法的经济调度新算法

提出基于简单排序法（simple ranking method）的经济调度（ED）最优算法和近似算法。在数学模型中考虑了功率平衡约束、机组最大最小出力约束以及机组爬坡速率约束。算法没有引入任何乘子,因此计算中不存在震荡现象,并且单调收敛,计算速度很快。文中给出了各算法的数学模型和计算流程,并用20机系统对算法进行了验证。计算结果验证了算法的有效性和实用性。