变负荷条件下追踪电力系统安全最优运行轨迹的参数化方法

提出一种追踪线性约束下凸可分规划问题最优解轨迹的参数化方法。该参数优化算法可在对偶松弛凸可分规划算法的主循环之外,通过少量参数化扩展得到。参数分析表明最优解轨迹的性态是一条分段线性曲线,解轨迹上的破点和不可行现象存在密切关系。将这种方法应用到电力系统有功最优潮流问题中,得到一种统一经济调度和安全约束调度的参数化安全约束调度(security constrained economic dispatch,SCED)新算法,它可快速追踪变负荷条件下系统安全最优运行轨迹。算法在IEEE14-300节点测试系统及2个省级实际系统上通过测试,数值试验和几何分析表明了该方法的计算特性和物理内涵,同时清楚地显示了目前调度模式中存在的问题和改进方向。     

暂态稳定安全经济代价计算

根据暂态稳定裕度对节点有功、无功功率及变压器运行方式变化的灵敏度分析结果,以有功、无功电费最小为目标函数,构造了适用于合同交易与非合同交易共存的电力市场安全预防再调度和安全校正再调度数学模型,此模型可用线性规划求解。此方法能用于计算为提高电力系统暂态安全性而须付出的经济代价,经济代价可用于最佳可靠性指标研究。根据稳定裕度对节点功率的灵敏度来考虑系统安全约束比采用联络线潮流约束更为可靠;考虑有功、无功管理再调度比只考虑有功调度可能更为经济。中给出了24节点系统实例分析结果。     

Dynamic environmental economic dispatch using multiobjective differential evolution algorithm with expanded double selection and adaptive random restart

The dynamic environmental economic dispatch (DEED) model is presented in this paper, in which the fuel cost and emission effect over a certain period of time are optimized as conflicting objectives. It is a high dimensional, nonlinear constrained multiobjective optimization problem when generators’ valve point effect, ramp rate limits and power load variation are considered. This paper proposes a modified adaptive multiobjective differential evolution (MAMODE) algorithm to solve the problem. In MAMODE, expanded double selection and adaptive random restart operators are proposed to modify the evolutionary processes for avoiding premature and a dynamic heuristic constraint handling (DHCH) approach is introduced to deal with the complicated constraints. The DHCH can lessen infeasible solutions gradually. To illustrate the effectiveness of the method, four cases based on three test power systems are studied. The simulation result indicates that the DEED can be solved quickly. Comparison of numerical results demonstrates the proposed method has higher performance.     

基于实用化安全约束经济调度扩展建模策略

安全约束经济调度是提高电网运行可靠率,实现节能减排,提高调度计划精细化管理水平的有效技术手段。现有安全约束经济调度研究多集中在常见目标与约束建模以及优化算法等方面,较少考虑实际生产因素,因此计划结果执行率偏低,安全约束经济调度在实际生产中实用化困难。针对上述问题,针对计划编制的优化目标,“三公”调度、计划出力曲线形状以及基础数据区间处理等实际需求,提出了基于实用化的安全约束经济调度扩展模型。将所提的建模策略应用于多个生产实例,证明了所提模型在增强“三公”调度准确率、改善计划出力曲线形状以及提高计划结果执行率上有着较好的工程实用性。     

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.     

Combined economic and emission dispatch problems using biogeography-based optimization

In this work, biogeography-based optimization (BBO) is presented for solving different constrained economic load dispatch (ELD) problems combined with economic emission aspects in power system. Nonlinear characteristics of generators like valve point discontinuities, ramp rate limits and prohibited operating zones are considered in the problem. The simulation results show that the proposed BBO algorithm based solutions prove to be the best near-global optimal as compared to the solutions based on Newton–Raphson, Tabu search, genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA), fuzzy logic controlled genetic algorithm (FCGA), particle swarm optimization (PSO) and differential evolution (DE).     

Unit commitment by an enhanced simulated annealing algorithm

A new simulated annealing (SA) algorithm combined with a dynamic economic dispatch method has been developed for solving the short-term unit commitment (UC) problem. SA is used for the scheduling of the generating units, while a dynamic economic dispatch method is applied incorporating the ramp rate constraints in the solution of the UC problem. New rules concerning the tuning of the control parameters of the SA algorithm are proposed. Three alternative mechanisms for generating feasible trial solutions in the neighborhood of the current one, contributing to the reduction of the required CPU time, are also presented. The ramp rates are taken into account by performing either a backward or a forward sequence of conventional economic dispatches with modified limits on the generating units. The proposed algorithm is considerably fast and provides feasible near-optimal solutions. Numerical simulations have proved the effectiveness of the proposed algorithm in solving large UC problems within a reasonable execution time.     

A new algorithm for on-line security constrained economic dispatch

A new approach, the constant reduced Hessian matrix (CRHM) algorithm for the on-line security constrained economic dispatch (OSED) problem, is presented in this paper. The proposed method, in which repeating the AC load flow program has been avoided, satisfies both load flow equations and security limits exactly. The computational speed and the excellent convergence of this algorithm are demonstrated by applying it to a sample system.     

A security constrained environmental/economic power dispatch technique using F-MSG algorithm for a power system area including limited energy supply thermal units

A security constrained non-convex environmental/economic power dispatch problem for a lossy electric power system area including limited energy supply thermal units is formulated. An iterative solution method based on modified subgradient algorithm operating on feasible values (F-MSG) and a common pseudo scaling factor for limited energy supply thermal units are used to solve it. In the proposed solution method, the F-MSG algorithm is used to solve the dispatch problem of each subinterval, while the common pseudo scaling factor is employed to adjust the amount of fuel spent by the limited energy supply thermal units during the considered operation period. We assume that limited energy supply thermal units are fueled under take-or-pay (T-O-P) agreement.The proposed dispatch technique is demonstrated on IEEE 30-bus power system with six thermal generating units having non-convex cost rate functions. Two of the generating units are selected as gas-fired limited energy supply thermal units. Pareto optimal solutions for the power system, where the constraint on the amount of fuel consumed by the limited energy supply thermal units is not considered, are calculated first. Later on, the same Pareto optimal solutions for the power system, where the fuel constraint is considered, are recalculated, and the obtained savings in the sum of optimal total fuel cost and total emission cost are presented. The dispatch problem of the first subinterval of the test system was solved previously by means of differential evolution (DE), and a hybrid method based on combination of DE and biogeography based optimization (BBO) for the best cost and the best emission cases in the literature. The results produced by these methods are compared with those of produced by the proposed method in terms of their total cost rate, emission rate and solution time values. It is demonstrated that the proposed method outperforms against the evolutionary methods mentioned in the above in terms of solution time values especially when the exact model of the test system is considered.     

Economic dispatch with security-constrained rescheduling

A mathematical framework is described for the solution of the economic dispatch problem with security constraints, which can take into account the system corrective capabilities after an outage has occurred. The solution algorithm is based on mathematical programming decomposition techniques that allow the iterative solution of a ‘base-case’ economic dispatch and separate contingency analysis with generation rescheduling to eliminate constraint violations. The resulting dispatch has the same security level as the usual security-constrained dispatch, but with lower operating costs. Case studies with the system of Southern Brazil are presented. The extension of the methodology to include other corrective schemes is also discussed.     

基于启发式线性规划的大规模安全约束调度快速求解方法

提升大规模安全约束经济调度优化模型的求解性能是开展大电网跨省区电力电量全局优化平衡的前提与基础。首先分析问题的物理特性,通过并行计算求解不考虑机组爬坡约束的分时段约束松弛模型。基于对松弛解的分析获得可用于指导安全约束经济调度模型改进的有用信息,以约束剔除和约束增加的方式提出了基于启发式线性规划的大规模安全约束经济调度快速求解方法。将所提算法运用于新英格兰10机扩展系统和中国实际电网,验证了所提算法的正确性和有效性。     

Application of pattern search method to power system security constrained economic dispatch with non-smooth cost function

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED) with non-smooth cost function. Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using three different test systems. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED). In addition, valve-point effect loading and total system losses are considered to further investigate the potential of the PS technique. Based on the results, it can be concluded that the PS has demonstrated ability in handling highly nonlinear discontinuous non-smooth cost function of the SCED.     

Differential evolution algorithm for emission constrained economic power dispatch problem

In this paper, a differential evolution (DE) algorithm is developed to solve emission constrained economic power dispatch (ECEPD) problem. Traditionally electric power systems are operated in such a way that the total fuel cost is minimized regardless of emissions produced. With increased requirements for environmental protection, alternative strategies are required. The proposed algorithm attempts to reduce the production of atmospheric emissions such as sulfur oxides and nitrogen oxides, caused by the operation of fossil-fueled thermal generation. Such reduction is achieved by including emissions as a constraint in the objective of the overall dispatching problem. A simple constraint approach to handle the system constraints is proposed. The performance of the proposed algorithm is tested on standard IEEE 30-bus system and is compared with conventional methods. The results obtained demonstrate the effectiveness of the proposed algorithm for solving the emission constrained economic power dispatch problem.     

基于改进多目标海樽群算法的电力系统优化调度

文中提出了一种新的多目标海樽群优化算法,将其与等式约束修正技术和可行解占优约束处理技术相结合,用于求解高度约束的电力系统环境经济优化调度问题。该算法采用高斯采样策略和变异操作增强其寻优性能;通过一种改进的基于动态拥挤距离的非支配排序方法获得分布均匀的帕累托最优前沿;应用模糊集理论为决策者提供最佳折中解。在IEEE 30节点6机组标准测试系统上进行算例仿真,并与其它优化算法进行了对比。结果表明,所提算法在求解电力系统环境经济调度问题时具有更好的优化效果。     

Optimal allocation of generation margin to cope with the expected line overloads

Allocation of sufficient regulating margin on each generator just before transmission line overloads enables the power system to obey quickly the security corrective actions. The rate at which the line flows can be reduced depends upon the generator operating point and its ramp limits. The time allowed to remove an overload depends upon the line rating and the magnitude of such an overload. If an overload is predicted by an emergency mode detector, the time required to alleviate this overload consists of two components: the time required to decide the suitable security corrective actions and the time required to perform these actions.In recent work by Farghal and others, a fast technique has been developed to alleviate the line overloads using sensitivity parameters evaluated from the base case before overloads, and so the few seconds needed for recalculation are saved. However, the second component of time with an order of a few minutes has still not been considered. In this paper, an attempt is made to minimize this time by proper allocation of system regulating margin just before an emergency.This paper proposes a method for the optimal allocation of system regulating margin employing Bender's decomposition principle coupled with a successive linearization technique. This method utilizes the existing package for economic dispatch as a master program and modifies the operating point of each generator output to allocate the suitable regulating margin according to the expected emergency in another subprogram with minimum cost increase. Thus, the method acts as a partial alternative to the expensive emergency start-up procedures.     

Low-carbon emission/economic power dispatch using the multi-objective bacterial colony chemotaxis optimization algorithm considering carbon capture power plant

To study the constrained emission/economic dispatch problem involving competing objectives in electric power systems with carbon capture system (CCS) technology, this paper proposes a multi-objective optimization approach based on bacterial colony chemotaxis (MOBCC) algorithm. In this algorithm, a Lamarckian constraint handling method based approach is improved to update the bacterial colony and the external archive. Finally, the optimization tests of the proposed algorithm are carried out in the IEEE 30-bus test system. Results demonstrate this approach has the advantage of dealing with highly non-linear and multi-objective functions of carbon capture thermal generator’s emission/economic dispatch problem.     

电网规划综合评判决策系统的设计与应用

提出了一种求解电力系统负荷经济分配问题的改进粒子群优化算法.该算法考虑了机组的爬坡约束、出力限制区约束、非光滑费用函数曲线等非线性特性,用保留可行解的方法处理负荷平衡约束条件,用自适应罚函数法处理爬坡和出力限制区约束条件,加快了算法的收敛速度,对不活动粒子的处理使算法避免了"早熟"现象.仿真计算表明,改进粒子群优化算法是一种求解负荷经济分配问题的有效方法.     

A homogeneous linear programming algorithm for the securityconstrained economic dispatch problem

This paper presents a study of the simplified homogeneous and self-dual (SHSD) linear programming (LP) interior point algorithm applied to the security constrained economic dispatch (SCED) problem. Unlike other interior point SCED applications that consider only the N security problem, this paper considers both (N-1) and (N-2) network security conditions. An important feature of the optimizing interior point LP algorithm is that it can detect infeasibility of the SCED problem reliably. This feature is particularly important in SCED applications since line overloading following a contingency often results in an infeasible schedule. The proposed method is demonstrated on the IEEE 24 bus test system and a practical 175 bus network. A comparison is carried out with the predictor-corrector interior point algorithm for the SCED problem presented previously (see ibid., vol. 12, no.2, p.803-10, 1997)     

A simple two stage optimization algorithm for constrained powereconomic dispatch

A simple two stage optimization algorithm is proposed and investigated for fast computation of constrained power economic dispatch control problems. The method is a simple demonstration of the hierarchical aggregation-disaggregation (HAD) concept. The algorithm first solves an aggregated problem to obtain an initial solution. This aggregated problem turns out to be classical economic dispatch formulation, and it can be solved in 1% of overall computation time. In the second stage, a linear programming method finds optimal solution which satisfies power balance constraints, generation and transmission inequality constraints and security constraints. Implementation of the algorithm for IEEE systems and EPRI Scenario systems shows that the two stage method obtains an average speedup ratio of 10.64 as compared to the classical LP-based method     

Security constrained economic dispatch using nonlinearDantzig-Wolfe decomposition

This paper proposes a new approach to the security constrained economic dispatch based on a nonlinear version of the Dantzig-Wolfe decomposition principle. The dispatch problem is formulated using truly nonlinear unit cost functions and a new, detailed representation of reserve curves. The solutions obtained by the method have the equal λ property. The proposed decomposition scheme, is more efficient as the number of generating units in the problem is increased. Numerical results obtained on three test cases are presented