Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network

This paper proposes an improved priority list (IPL) and augmented Hopfield Lagrange neural network (ALH) for solving ramp rate constrained unit commitment (RUC) problem. The proposed IPL-ALH minimizes the total production cost subject to the power balance, 15 min spinning reserve response time constraint, generation ramp limit constraints, and minimum up and down time constraints. The IPL is a priority list enhanced by a heuristic search algorithm based on the average production cost of units, and the ALH is a continuous Hopfield network whose energy function is based on augmented Lagrangian relaxation. The IPL is used to solve unit scheduling problem satisfying spinning reserve, minimum up and down time constraints, and the ALH is used to solve ramp rate constrained economic dispatch (RED) problem by minimizing the operation cost subject to the power balance and new generator operating frame limits. For hours with insufficient power due to ramp rate or 15 min spinning reserve response time constraints, repairing strategy based on heuristic search is used to satisfy the constraints. The proposed IPL-ALH is tested on the 26-unit IEEE reliability test system, 38-unit and 45-unit practical systems and compared to combined artificial neural network with heuristics and dynamic programming (ANN-DP), improved adaptive Lagrangian relaxation (ILR), constraint logic programming (CLP), fuzzy optimization (FO), matrix real coded genetic algorithm (MRCGA), absolutely stochastic simulated annealing (ASSA), and hybrid parallel repair genetic algorithm (HPRGA). The test results indicate that the IPL-ALH obtain less total costs and faster computational times than some other methods.     

基于最优场景生成算法的主动配电网无功优化

针对间歇性分布式电源输出功率的不确定性和随机性,提出采用Wasserstein距离指标和K-means聚类场景削减技术生成最优场景,将随机优化问题转换为确定性优化问题。建立了风—光—荷多场景树模型,并以有功网损最小、电压偏差最小作为目标函数,考虑储能荷电状态约束影响,建立含间歇性分布式电源的主动配电网无功优化数学模型,并采用人工蜂群算法对模型进行求解。仿真分析得出基于Wasserstein距离指标和K-means聚类场景削减技术生成的最优场景能较精确地体现分布式电源有功出力的随机特性。最后,以IEEE-33节点配电系统为例进行仿真分析,验证了所提方法的有效性和可行性。     

Optimization-based scheduling of hydrothermal power systems withpumped-storage units

This paper presents an optimization-based method for scheduling hydrothermal systems based on the Lagrangian relaxation technique. After system-wide constraints are relaxed by Lagrange multipliers, the problem is converted into the scheduling of individual units. This paper concentrates on the solution methodology for pumped-storage units. There are, many constraints limiting the operation of a pumped-storage unit, such as pond level dynamics and constraints, and discontinuous generation and pumping regions. The most challenging issue in solving pumped-storage subproblems within the Lagrangian relaxation framework is the integrated consideration of these constraints. The basic idea of the method is to relax the pond level dynamics and constraints by using another set of multipliers. The subproblem is then converted into the optimization of generation or pumping; levels for each operating state at individual hours, and the optimization of operating states across hours. The optimal generation or pumping level for a particular operating state at each hour can be obtained by optimizing a single variable function without discretizing pond levels. Dynamic programming is then used to optimize operating states across hours with only a few number of states and transitions. A subgradient algorithm is used to update the pond level Lagrangian multipliers. This method provides an efficient way to solve a class of subproblems involving continuous dynamics and constraints, discontinuous operating regions, and discrete operating states     

Augmented Lagrange Hopfield network based Lagrangian relaxation for unit commitment

This paper proposes an augmented Lagrange Hopfield network based Lagrangian relaxation (ALHN-LR) for solving unit commitment (UC) problem with ramp rate constraints. ALHN-LR is a combination of improved Lagrangian relaxation (ILR) and augmented Lagrange Hopfield network (ALHN) enhanced by heuristic search. The proposed ALHN-LR method solves the UC problem in three stages. In the first stage, ILR is used to solve unit scheduling satisfying load demand and spinning reserve constraints neglecting minimum up and down time constraints. In the second stage, heuristic search is applied to refine the obtained unit schedule including primary unit de-commitment, unit substitution, minimum up and down time repairing, and de-commitment of excessive units. In the last stage, ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian relaxation is applied to solve constrained economic dispatch (ED) problem and a repairing strategy for ramp rate constraint violations is used if a feasible solution is not found. The proposed ALHN-LR is tested on various systems ranging from 17 to 110 units and obtained results are compared to those from many other methods. Test results indicate that the total production costs obtained by the ALHN-LR method are much less than those from other methods in the literature with a faster manner. Therefore, the proposed ALHN-LR is favorable for large-scale UC implementation.     

Optimal reactive dispatch through primal-dual method

This paper presents an algorithm for the optimal reactive dispatch problem. The algorithm is based on Newton's method which it works with an augmented Lagrangian function associated with the original problem. The function aggregates all the equality and inequality constraints. The first order necessary conditions for optimality are reached by Newton's method, and by updating the dual variables and the penalty terms associated with the inequality constraints. The proposed approach does not have to identify the set of binding constraints and can be utilized for an infeasible starting point. The sparsity of the Hessian matrix of the augmented Lagrangian is completely exploited in the computational implementation. Tests results are presented to show the good performance of this algorithm     

Large-scale application of the Han-Powell algorithm to compact models of static and dynamic dispatch of real power

In this study some second-order algorithms derived from the Han-Powell method are applied to real power optimization both in a static and in a dynamic dispatch procedure with security constraints. These procedures employ suitable compact reduced models for large-scale applications. In the dynamic approach a time-varying load is shared among the control units by adopting a discrete formulation of the dispatch problem. This involves the subdivision of the optimization interval into a certain number of sub-intervals with constant loads and the addition, to the ordinary constraints of the static approach, of dynamic constraints on rate of change of MW output of thermal units. In particular, security constraints are modified in order to take into account their dependence on the load variability during the optimization interval. Also in the paper, a dynamic approach is shown to be needed for preventive scheduling of the thermal generation during the time periods characterized by a high rate of load variation (pick-up or drop-down hours) as well as during the online rescheduling. The robustness and the efficiency of the adopted procedures have been demonstrated by several tests on a sample network of small dimension as well as on large-scale systems. In the dynamic approach a suitably modified version of the Han-Powell algorithm is adopted which employs an alternative technique in the construction and in the updating of the Hessian matrix of the Lagrangian function. This allows us to handle large-scale problems arising from the optimization of a large system on the framework of a minute subdivision of the dispatch interval. This technique exploits and conserves in the updating phase the sparseness property of the matrix, without using the usual Broyden-Fletcher-Shanno-Goldfarb formulae.     

An enhanced Lagrangian neural network for the ELD problems with piecewise quadratic cost functions and nonlinear constraints

This paper presents a new Lagrangian artificial neural network (ANN) and its application to the power system economic load dispatch (ELD) problems with piecewise quadratic cost functions (PQCFs) and nonlinear constraints. By restructuring the dynamics of the modified Lagrangian ANN [IEEE ICNN, 1 (1996) 537], stable convergence characteristics are obtained even with the nonlinear constraints. The convergence speeds are enhanced by employing the momentum technique and providing a criteria for choosing the learning rate parameters. Instead of having one convex cost function for each unit, which is normally the case in typical ELD problem formulations, more realistic multiple quadratic cost functions are used to reflect the effects of valve point loadings and possible fuel changes. In addition, the B matrix approach is employed for more accurate estimation of the transmission losses than treating them as a constant, which necessitate the inclusion of a nonlinear equality constraint. The effectiveness of the proposed ANN applied to the ELD problem is demonstrated through extensive simulation tests.     

考虑交流潮流约束的机组组合并行解法

针对传统机组组合模型的种种不足,该文提出了一种考虑交流潮流约束及静态安全约束的机组组合模型,并给出了一种完整的并行化解法。该法借助于扩展拉格朗日松弛法和变量复制技术,将原问题转换为其对偶问题,并利用附加问题原理将对偶问题分解为动态规划和最优潮流(OPF)子问题。对于OPF子问题,采用鲁棒性好、收敛速度快的预测校正内点法求解,同时在求解过程中,采用并行处理技术。IEEE118节点及IEEE300节点仿真结果表明,该方法收敛性好,非常适合并行处理。     

Efficient integer optimization algorithms for optimal coordinationof capacitors and regulators

The optimal coordination of switched capacitors and tap-changing transformers in a radial distribution system is considered. The formulation incorporates voltage constraints. The coordination problem is approximated by a constrained discrete quadratic optimization using the results from the corresponding unconstrained continuous problem. The discrepancy between the actual and approximating problem is discussed. Two algorithms are proposed to seek solutions to the approximating optimization problem. The first is a randomized algorithm that runs fast but for which there is no guarantee of optimality. The second is a deterministic algorithm, the run time of which is polynomially bounded in the problem size. For large systems the run times of these algorithms may be significantly less than the run times of explicit search or branch and bound algorithms. Test results on a 70 node system confirm the theoretical predictions     

Modified Newton method for reactive dispatching

This paper describes a new approach to the optimal reactive dispatch problem, based on an augmented Lagrangian function of the original problem. The Karush–Kuhn–Tucker (KKT) optimality conditions are solved by the modified Newton method. The second-order information in the original system of equations is approximated and the first-order information is kept intact The proposed method requires less computer memory than those algorithms currently available. The effectiveness of the proposed approach has been examined by solving the IEEE 30-bus and the BRAZILIAN 810-bus systems.     

Hydrothermal scheduling by augmented Lagrangian: consideration oftransmission constraints and pumped-storage units

This paper presents an augmented Lagrangian (AL) approach to scheduling a generation mix of thermal and hydro resources. AL presents a remedy to duality gap encountered with the ordinary Lagrangian for nonconvex problems. It shapes the Lagrangian function as a hyperparaboloid associating penalty in the direction of the coupling constraints. This work accounts further for the transmission constraints. We use a hydrothermal resource model with pumped-storage units. An IEEE 24-bus test system is used for AL performance illustration. Computational models are all coded in C. The results of the test case show that the AL approach can provide better scheduling results as it can detect optimal on/off schedules of units over a planning horizon at a minimal cost with no constraint violation. It requires no iteration with economic dispatch algorithms. The approach proves accurate and practical for systems with generation diversity and limited transmission capacity     

基于自适应系统优化算法的机组组合

算法采用系统分解理论将系统约束松弛,把机组组合问题分解为2层优化问题.上层通过拉格朗日乘子的自适应调整来协调单个机组的子系统,下层采用遗传算法求解单个机组独立的子系统优化问题.对拉格朗日乘子的自适应调整明显减少了对偶间隙的振荡现象,对遗传算法中交叉变异算子自适应的调整有效地克服了早熟现象.算例表明可行解的质量高、收敛速度快,与传统算法相比具有更高的自适应性,适用于大规模、复杂系统的机组组合问题的求解.     

A multi-agent technique for contingency constrained optimal powerflows

This paper does three things. First, it proposes that each critical contingency in a power system be represented by a “correction time” (the time required to eliminate the violations produced by the contingency), rather than by a set of hard constraints. Second, it adds these correction times to an optimal power flow and decomposes the resulting problem into a number of smaller optimization problems. Third, it proposes a multi-agent technique for solving the smaller problems in parallel. The agents encapsulate traditional optimization algorithms as well as a new algorithm, called the voyager, that generates starting points for the traditional algorithms. All the agents communicate asynchronously, meaning that they can work in parallel without ever interrupting or delaying one another. The resulting scheme has potential for handling power system contingencies and other difficult global optimization problems     

基于广义主从分裂的输配电网一体化分布式无功优化方法

大量分布式电源接入配电网后,输、配电网间无功电压关系更加密切,传统输、配电网无功优化孤立进行已不再合适。根据输、配电网运行管理的独立性,提出了一种基于广义主从分裂思想的输配电网一体化分布式无功优化方法。输配全局无功优化问题分解为输电网优化主子问题、各配电网优化从子问题及边界一致性判别问题。各子网无功优化子问题采用对偶规划类算法求解,离散变量采用罚函数法处理以保持增广拉格朗日函数的可微性。通过由对偶乘子构造的边界灵敏度实现输、配电网子问题间的解耦,输配电网控制中心间通过传递边界变量及其灵敏度信息实现分布式协调。对IEEE 30节点系统(输电网)和含多种分布式电源的IEEE 33节点系统(配电网)进行仿真,验证了所提方法的有效性。     

Optimal allocation,sizing of PHEV parking lots in distribution system

The emerging of plug-in-hybrid electric vehicles (PHEV) results in the increase in the utilization of vehicles batteries for grid support. This paper presents a multi-objective algorithm to optimally determine the number of parking lots to be allocated in a distribution system. In addition, the algorithm optimally selects the locations and sizes of these parking lots. The proposed algorithms determine also the corresponding energy scheduling of the system resources. The objective of the proposed algorithm is to minimize the overall energy cost of the system. The problem is formulated as an optimization problem which is solved using artificial bee colony (ABC) and firefly algorithm taking into consideration the power system and PHEV operational constraints. The proposed algorithms are applied to a 33-bus radial distribution network. The test results indicate an improvement in the operational conditions of the system.     

Performance assessment of PSO,DE and hybrid PSO–DE algorithms when applied to the dispatch of generation and demand

This work presents a comparison of three evolutionary algorithms, the particle swarm optimization, the differential evolution algorithm and a hybrid algorithm derived from the previous, when applied to the generation and demand dispatch problem. An optimization problem is formulated in the context of a small grid with partially flexible demand that can be shifted along a time horizon. It is assumed that grid operator dispatches generation and flexible demand along the time horizon aiming at minimizing generation costs. Consumption restrictions associated with flexible demand are modeled by equality and inequality energy constraints. Power flow equality constraints and inequality constraints due to operational limits for each dispatch interval are represented. The paper discusses a methodology for evolutionary algorithms performance assessment and states the importance of using statistical tools. The comparison is initially conducted using the IEEE 30-bus test system. Problem dimension effect is addressed considering different number of dispatch intervals in the time horizon. Moreover, the algorithms are applied to the 192-bus system of a Brazilian distribution utility, in the particular context of a load management program for large consumers of the company. In this application, the quality of the near-optimal solution obtained with the stochastic algorithms is evaluated by comparing with an analytical optimization algorithm solution.     

An adaptive chaotic artificial bee colony algorithm for short-term hydrothermal generation scheduling

Short-term hydrothermal scheduling (SHS) is a complicated nonlinear optimization problem with a set of constraints, which plays an important role in power system operations. In this paper, we propose to use an adaptive chaotic artificial bee colony (ACABC) algorithm to solve the SHS problem. In the proposed method, chaotic search is applied to help the artificial bee colony (ABC) algorithm to escape from a local optimum effectively. Furthermore, an adaptive coordinating mechanism of modification rate in employed bee phase is introduced to increase the ability of the algorithm to avoid premature convergence. Moreover, a new constraint handling method is combined with the ABC algorithm in order to solve the equality coupling constraints. We used a hydrothermal test system to demonstrate the effectiveness of the proposed method. The numerical results obtained by ACABC are compared with those obtained by the adaptive ABC algorithm (AABC), the chaotic ABC algorithm (CABC) and other methods mentioned in literature. The simulation results indicate that the proposed method outperforms those established optimization algorithms.     

考虑网络安全约束的机组组合新算法

市场机制驱使电网运行于安全极限的边缘,考虑网络安全约束的机组组合问题变得尤为重要,基于对偶原理的拉格朗日松弛法是解决这一问题的有效途径。文章提出了一种解决网络安全约束下的机组组合问题的新算法,在拉格朗日对偶分解的基础上结合变量复制技术,通过引入附加人工约束将网络约束嵌入单机子问题中,实现在机组组合中考虑网络安全约束。该算法摆脱了现有各种处理手段在解决网络安全约束的机组组合问题时将网络安全约束与机组启停相分离的不足,揭示了安全经济调度和安全约束下的机组组合在概念上的区别和联系。     

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。     

Weighted least absolute value power system state estimation using rectangular coordinates and equivalent measurement functions

This paper presents a new efficient computation technique for robust power system state estimation based on weighted least absolute value (WLAV) criterion. The proposed method employs rectangular form of state variables and equivalent measurements technique in order to obtain the linear measurement functions with linear constraints of state variables. The state estimation problem is then formulated as an optimization problem with a set of equality and inequality constraints. A solution method based on interior point algorithm is also proposed. Tests with several IEEE standard systems have been performed to investigate the performance of the proposed algorithm. Results indicate that the proposed state estimator gives promising performance compared with weighted least square (WLS) based estimation algorithms using state variables in polar forms. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.