Evolutionary Programming-Based Multiarea Economic Dispatch with Tie Line Constraints

This paper presents a new approach to include tie line constraints in multiarea economic dispatch problems by using evolutionary programming (EP). The proposed method always finds the global or near global optimum for small and reasonable-sized multiarea economic dispatch (MAED) problems. The inclusion of tie line constraints to MAED does not introduce any complexity in the approach. The applicability and validity of the proposed method is shown by implementing it on three example systems - 2, 4, and 14 areas - and their results are compared with those obtained by classical economic dispatch, network flow programming, and dynamic programming methods, respectively. The results show that the proposed method can serve as a potential tool for solving MAED problems.     

Neural networks approach for solving economic dispatch problem withtransmission capacity constraints

This study presents a new approach using Hopfield neural networks for solving the economic dispatch (ED) problem with transmission capacity constraints. The proposed method is based on an improved Hopfield neural network which was presented by Gee et al. (1994). The authors discussed a new mapping technique for quadratic 0-1 programming problems with linear equality and inequality constraints. The special methodology improved the performance of Hopfield neural networks for solving combinatorial optimization problems. The authors have now modified Gee and Prager's (GP) method in order to solve ED with transmission capacity constraints. Constraints are handled using a combination of the GP model and the model of Abe et al. (1992). The proposed method (PHN) has achieved efficient and accurate solutions for two-area power systems with 3, 4, 40 and 120 units. The PHN results are very close to those obtained using the quadratic programming method     

Economic dispatch with prohibited operating zones using fast computation evolutionary programming algorithm

This paper presents an efficient and simple approach for solving the economic dispatch (ED) problem with units having prohibited operating zones. The operating region of the units having prohibited zones is broken into isolated feasible sub-regions which results in multiple decision spaces for the economic dispatch problem. The optimal solution will lie in one of the feasible decision spaces and can be found using the conventional λ–δ iterative method in each of the feasible decision spaces. But, this elaborate search procedure is time consuming and not acceptable for on-line application. In this paper, a simple and novel approach is proposed. In this approach, the optimal solution and the corresponding optimum system lambda are determined using an efficient fast computation evolutionary programming algorithm (FCEPA) without considering the prohibited operating zones. Then, a small set of advantageous decision spaces is formed by combining the feasible sub-regions of the fuel cost curve intervening the prohibited zones in the neighbourhood of the optimal system lambda. A penalty cost for each advantageous decision space is judiciously computed using participation factor. The most advantageous decision space is found out by comparing the penalty cost of the decision spaces. The optimal solution in the most advantageous decision space is obtained using the FCEPA. The proposed algorithm is tested on a number of sample systems with units possessing prohibited zones. The study results reveal that the proposed approach is computationally efficient and would be a competent method for solving economic dispatch problem with units having prohibited operating zones.     

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     

Hierarchical economic dispatch for multi-area power systems

In a multi-area power system, power exchange through tie lines such that the overall cost of the system operation is a minimum is a major economic dispatch problem. In this paper, techniques and methods are presented for solving the economic dispatch problem of radially interconnected power systems. The proposed method, based on a multi-area approach, uses an hierarchical control concept to improve the computation efficiency and accuracy; it has certain advantages over the conventional single-area approach. Theoretical formulations are derived and discussed from a simple power transfer concept. An efficient algorithm is organized. Numerical examples have been tested for a fictitious three-area system. The simulation results strongly support the proposed method with real-time application capability.     

Multi-area power systems economic dispatch using nonlinear convex network flow programming

This paper presents a new nonlinear convex network flow programming (NLCNFP) model and algorithm for solving the security-constrained multi-area economic dispatch (MAED) problem. The tie-line security and transfer constraints in each area are considered in the MAED model. A simple analysis of a buying and selling contract in a multi-area environment is also made. The NLCNFP model of security-constrained multi-area economic dispatch was set up and solved by using a combined method of quadratic programming (QP) and network flow programming (NFP). The concept of maximum basis in the network flow graph was introduced to change the constrained model into an unconstrained QP model, which was easily solved by the reduced gradient method. The proposed approach is tested on a system of four interconnected areas with satisfactory results.     

Security constrained economic load dispatch using improved particle swarm optimization suitable for utility system

The objective of this paper is to evolve simple and effective methods for the economic load dispatch (ELD) problem with security constraints in thermal units, which are capable of obtaining economic scheduling for utility system. In the proposed improved particle swarm optimization (IPSO) method, a new velocity strategy equation is formulated suitable for a large scale system and the features of constriction factor approach (CFA) are also incorporated into the proposed approach. The CFA generates higher quality solutions than the conventional PSO approach. The proposed approach takes security constraints such as line flow constraints and bus voltage limits into account. In this paper, two different systems IEEE-14 bus and 66-bus Indian utility system have been considered for investigations and the results clearly show that the proposed IPSO method is very competent in solving ELD problem in comparison with other existing methods.     

基于粒子群算法的火电厂机组负荷优化分配研究

负荷优化分配是火电厂运行优化的一个重要研究领域,在机组之间合理地优化分配负荷能够提高整个火电厂运行的经济性。针对火电厂实际的运行情况,考虑多个实际约束条件,建立了并行火电机组间连续多时段动态负荷优化分配的数学模型;提出运用新近发展起来的智能算法-粒子群算法来解决动态负荷优化分配问题,详细介绍和研究了该算法的基本原理以及在负荷优化分配问题上的实现过程,并针对原算法的不足,对算法进行了改进;根据负荷分配和算法的特性,对初始种群的生成方法进行了改进,同时对约束条件进行了有效处理。仿真实例表明,该方法收敛性好,收敛速度快,能够有效地达到或接近全局最优,从而为火电厂机组负荷优化分配的求解提供了新的有效算法。     

Artificial immune system for dynamic economic dispatch

Dynamic economic dispatch determines the optimal scheduling of online generator outputs with predicted load demands over a certain period of time taking into consideration the ramp rate limits of the generators. This paper proposes artificial immune system based on the clonal selection principle for solving dynamic economic dispatch problem. This approach implements adaptive cloning, hyper-mutation, aging operator and tournament selection. Numerical results of a ten-unit system with nonsmooth fuel cost function have been presented to validate the performance of the proposed algorithm. The results obtained from the proposed algorithm are compared with those obtained from particle swarm optimization and evolutionary programming. From numerical results, it is found that the proposed artificial immune system based approach is able to provide better solution than particle swarm optimization and evolutionary programming in terms of minimum cost and computation time.     

基于分布式协同粒子群优化算法的电力系统无功优化

该文提出一种新颖的用于求解无功优化问题的分布式协同粒子群优化算法.考虑到大规模电力系统集中优化难度较大,采用分层控制中的分解-协调思想将大系统分解成若干个独立的子系统,有效地降低求解问题的复杂度,并采用混合策略在各子系统问进行协同进化.此外,子系统的无功优化采用了一种改进的粒子群优化算法,考虑了更多粒子的信息,能有效地提高算法的收敛精度和计算效率.对4个不同大小规模的系统进行的仿真计算结果表明该文提出的方法能够获得高质量的解,并且计算时间短,效率高,适合求解大规模电力系统的无功优化问题.     

基于最优决策树的多能系统快速鲁棒优化调度

新能源渗透率的持续增长造成了多能系统快速协调调度的巨大挑战,包括调度结果过于保守以及日内调度低效等问题。为此,提出了一种基于最优决策树分布式鲁棒优化的多能系统协调快速调度方法,所构建模型考虑电网日内经济调度,引入基于范数约束的概率分布置信集精准描述新能源的不确定性,防止调度结果过于保守。同时,根据新能源日内运行数据,分别通过可解释的最优分类树和最优回归树算法,优化日内机组启停状态和出力水平的初始决策量,解决日内鲁棒调度的低效问题。在四川某地区电网的验证结果表明,该模型可在兼顾调度成本和鲁棒性的同时,实现水风光多能系统的日内快速协调调度。     

利用拉格朗日松弛法解决SIS中的负荷经济分配问题

利用拉格朗日松弛法对火力发电厂厂级监控信息系统(SIS)中的负荷经济分配问题进行了求解。该方法以发电费用为目标函数,用拉格朗日乘子将系统的负荷约束松弛,并将得到的拉格朗日函数分解为一个上下两层的优化问题分别进行求解,保证了算法的快速有效性。与混沌优化及遗传算法进行了仿真比较,结果表明所提出的方法收敛速度快,求解精度高,易于掌握,是解决电力系统负荷经济分配问题的有效手段。     

Reserve constrained economic dispatch with prohibited operatingzones

A method is described for solving the reserve constrained economic dispatch problem when some of the online generating units have prohibited operating zone(s). For a unit with prohibited zone(s), the zone(s) divide the operating region between the minimum generation limit (Pmin) and the maximum generation limit (Pmax) into disjoint convex subregions. These disjoint subregions form a nonconvex decisions space and the associated economic dispatch problem is thus a nonconvex optimization problem. As a result, the conventional Lagrangian relaxation (LR) approach (e.g. the λ-δ iterative approach) cannot be applied directly. The method proposed decomposes the nonconvex decision space into a small number of subsets such that each of the associated dispatch problems is either infeasible or one that can be directly solved via the conventional LR approach. Based on the decomposition, the optimal solution is the least costly one among all the feasible solutions of the associated dispatch problems. Examples are also given to illustrate the proposed method     

A New Approach to Economic Dispatching Using Load Bus Elimination Techniques

This paper presents a new technique to solving the economic dispatch problem based on a reduced order model of the original system. Loads are first modeled by their appropriate voltage-dependent models as load admittances. Load admittances are then added to the bus admittance matrix and their respective buses are eliminated. The obtained model is a reduced model of the original system. The admittance matrix is of the same order as the number of voltagecontrolled buses in the system. The variables of the reduced model are the voltage-controlled buses’ angles and active power generations. Newton Raphson method is used to calculate the angles and active generations of the reduced model while minimizing the operational cost. Load bus voltages and angles of the original system are then calculated by a direct method and load admittances are modified. The process is repeated until convergence is achieved. The simulation is carried out on IEEE 118 bus test system. A comparison between the new approach and the penalty factors method has been made. It is shown that operational cost is improved and solution time is significantly reduced when compared to the penalty factors method of economic dispatch.     

A new model and algorithm of secure and economic automatic generation control

This paper presents a new nonlinear convex network flow programming (NLCNFP) model and algorithm for solving the on-line economic power dispatch and automatic generation control (AGC) with security and economy. Two AGC functions—load frequency control (LFC) and economic dispatch control (EDC) are modeled on the same timescale as EDC. This new AGC modeling and solution algorithm meets not only the control requirement of frequency and tie-line power as in the conventional load frequency control, but also the line security and system economy. The proposed approach is tested on an IEEE 30-bus system with satisfactory results.     

Emerging solution of large-scale unit commitment problem by Stochastic Priority List

This paper presents a new approach for unit commitment problem using Stochastic Priority List method. In this method, rapidly some initial unit commitment schedules are generated by Priority List method and priority based stochastic window system. Excess units are added with system dependent probability distribution to avoid overlooking a desired solution during repeated search. Constraints are not considered in this stage. Then schedules are modified gradually using the problem specific heuristics to fulfill constraints. To reduce calculations, heuristics are applied only to the solutions, which can be expected to improve. Besides, sign vector is introduced to reduce economic load dispatch (ELD) overhead recalculations. This process is repeated for optimal solution. The proposed method is tested using the reported problem data set. Simulation results for the systems up to 100-unit are compared to previous reported results. Numerical results show an improvement in solution cost and time compared to the results obtained from Genetic Algorithm and others.     

基于多方利益博弈的园区级综合能源系统经济优化运行技术研究

针对传统运行优化方法难以充分满足综合能源系统中多方参与主体的利益诉求,以及多目标求解筛选技术在其中的应用亟待进一步完善等问题,提出了考虑多方利益诉求的集中式优化模型和相应的新型求解筛选方法。首先,综合考虑新能源供应商、综合能源服务商和用户三方的收益,并计及综合需求响应的影响,构建了园区级综合能源系统经济优化调度模型;然后以NSGA-III算法为基础,用NSGA-II算法优化先知种群并引入带全局存档策略,提出了改进型NSGA-III算法;最后,利用模糊隶属度函数和改进模糊C均值算法,提出了基于满意度和聚类分析的混合筛选策略。研究结果表明:提出的综合能源系统经济优化运行方法性能优异,运用该方法所得的新能源消纳和综合需求响应均达到了较高的水平,求出的调度方案利益分布更加均匀。论文研究可为综合能源系统经济优化运行提供参考。     

Large-scale economic dispatch by genetic algorithm

This paper presents a new genetic approach for solving the economic dispatch problem in large-scale power systems. A new encoding technique is developed. The chromosome contains only an encoding of the normalized system incremental cost in this encoding technique. Therefore, the total number of bits of chromosome is entirely independent of the number of units. The salient feature makes the proposed genetic approach attractive in large and complex systems which other methodologies may fail to achieve. Moreover, the approach can take network losses, ramp rate limits, and prohibited zone avoidance into account because of genetic algorithm's flexibility. Numerical results on an actual utility system of up to 40 units show that the proposed approach is faster and more robust than the well-known lambda-iteration method in large-scale systems     

基于粒子群优化算法的AGC机组调配研究

电力市场下AGC机组的调配问题是辅助服务领域中的一个重要研究内容。提出了一种基于粒子群优化算法的AGC机组调配方案。该方法基于AGC机组调配的数学模型,考虑了机组调节容量,调节速率等约束条件。介绍了算法的基本原理,并分析了参数的不同取值对算法收敛性的影响。实际系统的算例表明,利用粒子群优化算法,不仅可以克服整数规划法可能得不到最优解的缺点,而且与遗传算法比较具有收敛性好,收敛速度快的优点,从而为AGC机组的调配问题提供了一种新的有效算法。     

Energy and reserve dispatch in a multi-zone electricity market

Competitive bidding for ancillary services (A/S), in addition to bidding for energy, is increasingly recognized as an important part of electricity markets. In this paper, an LP-based approach is presented for solving the multi-product (i.e. energy and A/S products), multi-zone/area physical market dispatch problem. The approach can explicitly represent various constraints, such as reserve requirement constraints, network security limits, and sharing of constrained resource capacity (e.g. maximum unit generation) between energy and reserve. The joint dispatch method, which dispatches energy and reserve market concurrently, is extended to allow inter-zonal reserve trading in a multi-zone competitive pool. Numerical examples are included to demonstrate the salient characteristics of the joint dispatch solution