计及校正控制的安全约束最优潮流的奔德斯分解算法

针对电力系统调度、规划、检修及风险评估中反复涉及的校正控制安全约束最优潮流的求解问题,在深入机制分析基础上,提出一种基于奔德斯(Benders)分解与协调的模型和算法,使复杂大电网的求解得以进行。该模型和算法的主要贡献体现在:对正常状态下的最优潮流问题(也称主问题),基于电网关键元件规律特性的变动形成有效约束,以提高其求解效率;对预想事件(也称子问题)集,基于处于主导地位预想事件概念的有效筛选方法,使子问题数显著减少。由此,借用奔德斯分解的处理思想,实现主问题与子问题间的协调机制。最后以IEEE 30节点标准系统以及山东电网445节点实际系统作为算例,对该算法进行可行性、有效性等验证。     

A Framework for Economic Load Frequency Control Design Using Modified Multi-objective Genetic Algorithm

This article deals with the coordination of security-constrained economic dispatch and load frequency control in an interconnected power system. The realistic and performance optimization inherent of the load frequency control (LFC) and security-constrained economic dispatch are fully considered without simplifying assumptions. For this purpose, modeling security-constrained economic dispatch as a discontinuous control action in the continuous frequency response model of a power system is well addressed. Considering conflict behavior of LFC and security-constrained economic dispatch beside the powerfulness of the multi-objective genetic algorithm (GA) to solve high-dimensional problems with conflicted objective functions makes it attractive for the automatic generation control coordination problem. The employed security-constrained economic dispatch utilizes the advantages of dynamic economic dispatch to achieve more realistic results. The GA is used to compute the decentralized control parameters and centralized generation levels of the on-line units to achieve an acceptable operating point. A significant modification in convergence speed has been performed by using LFC model properties in corporation with the genetic algorithm, so the proposed method gives considerable promise for implementation in multi-area power systems. The efficiency of the proposed algorithm and modification is demonstrated on a three control area power system.     

Security-constrained optimal generation scheduling for GENCOs

This paper presents an approach for maximizing a GENCO's profit in a constrained power market. The proposed approach considers the Interior Point Method (IPM) and Benders decomposition for solving the security-constrained optimal generation scheduling (SC-GS) problem. The master problem represents the economic dispatch problem for a GENCO which intends to optimize its profit. The formulation of the master problem does not bear any transmission network constraints. The subproblem will be used by the same GENCO to check the viability of its proposed bidding strategy in the presence of transmission network constraints. In this case if the subproblem does not yield a certain level of financial return for the GENCO or if the subproblem results in an infeasible solution of the GENCO's proposed bidding strategy, the GENCO will modify its proposed solution according to the Benders cuts that stem out of the subproblem. The study shows a more flexible scheduling paradigm for a GENCO in a competitive arena. The proposed approach proves practical for modeling the impact of transmission congestion on a GENCO's expected profit in a competitive environment.     

Flexible programming approach to security-constrained economic dispatch

An approach to the solution of security-constrained economic dispatch is proposed. A flexible programming technique is used which permits uncertainties in the load-demand profile to be taken into consideration in the determination of the optimal solution to economic dispatch under line-flow constraints. A linear-programming formulation of the security-constrained dispatch is the basis of this approach which provides not only the optimal dispatch policy but also the optimal amount of generation reserve needed to accommodate uncertainties in the load.     

A new hybrid approach for the solution of nonconvex economic dispatch problem with valve-point effects

Economic dispatch (ED) generally formulated as convex problem using optimization techniques by approximating generator input/output characteristic curves of monotonically increasing nature results in an inaccurate dispatch. The genetic algorithm has previously been used for the solution of problem for economic dispatch but takes longer time to converge to near optimal results. The hybrid approach is one of the methodologies used to fine tune the near optimal results produced by GA. This paper proposes new hybrid approach to solve the ED problem by using the valve-point effect. The approach we propose combines the genetic algorithm (GA) with active power optimization (APO) based on the Newton's second order approach (NSO). The genetic algorithm acts as a global optimizer giving near optimal generation schedule, which becomes the input for generation buses in APO algorithm. This algorithm acting as local search technique dispatching the generated active power of units for minimization of cost and gives optimum generation schedule. Three machines 6-bus, IEEE 5-machines 14-bus, and IEEE 6-mchines 30-bus systems have been tested for validation of our approach. Results of the proposed scheme compared with results obtained from GA alone give significant improvements in the generation cost showing the promise of the proposed approach.     

A simulated rebounding algorithm applied to the multi-stage security-constrained transmission expansion planning in power systems

This research discusses the multi-stage security-constrained transmission network expansion planning. In modern power systems, the problem is formulated as a large-scale, mixed-integer, non-linear programming problem, which for a real power systems is very difficult to solve. Although remarkable advances have been made in optimization techniques, finding an optimal solution to a problem of this nature can still be extremely challenging. In this paper, a new constructive heuristic approach, based on a local controlled random search (simulated rebounding algorithm) is proposed to choose the decision variables. The model can produce better solutions than other references techniques such as particle swarm optimization, evolutionary particle swarm optimization, genetic algorithms, and simulated annealing algorithm, among other evolutionary methods. The methodology is applied to assess the capabilities of the proposed approach in the Ecuadorian and Chilean Power Systems as an example of application. Simulation results show that the proposed approach is accurate and very efficient, and it has the potential to be applied to real power system planning problems. The algorithm has been presented and applied to the multi-stage security-constrained transmission expansion planning.     

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.     

互联电网安全约束经济调度场景构建方法

安全约束经济调度在省级电网调度控制中应用较为成熟。为实现大范围内资源优化配置,有必要研究互联电网安全约束经济调度技术。针对在实际生产运行中遇到的困难,提炼了优化目标设计、系统平衡、联络线调整、基础数据整合五个关键问题,并对每个问题给出多种解决策略。建立了基于策略组合的互联电网安全约束经济调度场景构建方法,分析了不同场景的适应性及对应模型特点。最后通过实际电网算例验证了策略组合的合理性和准确性。以实际需求为导向,构建不同的应用场景和经济调度模型,能提升互联电网安全约束经济调度技术的实用性和适应性。     

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.     

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     

A direct Newton-Raphson economic dispatch

The authors present a method to solve the real-time economic dispatch problem using an alternative Jacobian matrix considering system constraints. The transmission loss is approximately expressed in terms of generating powers and the generalized generation shift distribution factor. Based on this expression, a set of simultaneous equations of the Jacobian matrix are formulated and solved by the Newton-Raphson method. The proposed method eliminates the penalty factor calculation and solves the economic dispatch directly. The method resulted in a very fast solution speed and maintained good accuracy in test examples. It is a good approach to solve the economic dispatch problem     

Solving the unit commitment problem with a genetic algorithm through a constraint satisfaction technique

This paper proposes a genetic algorithm (GA) in conjunction with constraint handling techniques to solve the thermal unit commitment problem. To deal effectively with the constraints of the problem and prune the search space of the GA in advance, the difficult minimum up- and down-time constraints are embedded in the binary strings that are coded to represent the on-off states of the generating units. The other constraints are handled by integrating penalty factors into the cost function within an enhanced economic dispatch program. The proposed GA approach has been tested on a practical Taiwan Power (Taipower) thermal system over a 24-hour period for different utility factors and GA control parameters. Test results reveal that the features of easy implementation, fast convergence, and a highly near-optimal solution in solving the UC problem can be achieved by the proposed GA approach.     

考虑柔性交流输电系统设备控制的校正型安全约束最优潮流

为提升安全约束最优潮流调度的经济性与安全性,提出一种基于直流潮流的考虑柔性交流输电系统(FACTS)设备控制的校正型安全约束最优潮流模型。在线路故障发生后,通过FACTS设备校正措施,将线路潮流控制在其容许范围内。由于所提模型为大规模的非凸、非线性优化问题,难以直接求解,因此先采用大M法,将原非线性优化模型转换为混合整数线性规化模型,并采用Benders分解算法将转换后的模型分解为基态最优潮流主问题与N-1故障校验子问题。通过固定整数变量的方法,将非凸的混合整数优化子问题转换为线性规划子问题,从而能向主问题返回对应的Benders割。6节点系统与IEEE RTS-79节点系统算例验证了所提模型与算法的有效性。结果表明,考虑FACTS设备校正控制的安全约束最优潮流能有效提升调度运行的经济性。     

调峰辅助服务与电量协调优化的日内安全约束经济调度

大规模可再生能源的接入给电网调峰带来了巨大挑战,使得当前调度模式下发电机组均衡地完成其电量进度愈发困难。针对电网的日内调度计划,提出了调峰辅助服务与电量协调优化的日内调度模式,避免调峰服务市场机制与现有调度模式产生冲突。在该调度模式的基础上,建立了调峰辅助服务与电量协调优化的日内安全约束经济调度模型,实现了调峰资源与常规发电资源的协调调用,最优化系统的总调度成本。为了加速求解该调度模型,提出了以识别起作用安全约束为特征的迭代求解算法。最后,通过基于IEEE-30节点系统和实际省级电网的算例分析验证了所提模型方法的有效性、高效性与实用性。     

A hybrid genetic algorithm and bacterial foraging approach for dynamic economic dispatch problem

Dynamic economic dispatch (DED) is one of the most significant non-linear complicated problems showing non-convex characteristic in power systems. This is due to the effect of valve-points in the generating units’ cost functions, the ramp-rate limits and transmission losses. Hence, proposing an effective solution method for this optimization problem is of great interest. The original bacterial foraging (BF) optimization algorithm suffers from poor convergence characteristics for larger constrained problems. To overcome this drawback, a hybrid genetic algorithm and bacterial foraging (HGABF) approach is presented in this paper to solve the dynamic economic dispatch problem considering valve-point effects, ramp-rate limits and transmission losses. The HGABF approach can be derived by integrating BF algorithm and genetic algorithm (GA), so that the BF’s drawback can be treated before employing it to solve the complex and high dimensioned search space of the DED problem. To illustrate the effectiveness of the HGABF approach, several test systems with different numbers of generating units are used. The results of HGABF approach are compared with those obtained by other published methods employing same test systems. These results show the effectiveness and the superiority of the introduced method over other published methods.     

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.     

Dynamic economic dispatch using artificial immune system for units with valve-point effect

Dynamic economic dispatch (DED) is an important dynamic problem in power system operation and control. The objective of the problem is to schedule power generation for the online units over a time horizon, satisfying the unit and ramp-rate constraints. In this paper, clonal selection based artificial immune system (AIS) algorithm is used to solve the dynamic economic dispatch problem for generating units with valve-point effect. The feasibility of the proposed method is validated with ten and five unit test systems for a period of 24 h. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the robustness and proficiency of the proposed methodology over other existing techniques in terms of solution quality and computational efficiency.     

应用近似动态规划算法求解安全约束随机动态经济调度问题

针对大电网安全约束随机动态经济调度(DED)问题的求解时间太长,提出了应用近似动态规划算法快速求解不含抽水蓄能电站电网的安全约束随机DED问题的方法。建立了随机DED问题的虚拟存储器模型,以系统的正旋转备用容量作为存储变量,构建系统相邻时段的状态转移方程,并考虑了各输电线路和断面的安全约束。以风电场日前功率预测曲线为基础,通过拉丁超立方抽样产生风电场出力的误差场景,并逐一场景递推求解每个时段的二次规划模型以对各个时段的值函数进行训练,形成收敛的值函数,再代入预测场景求解以获得最终的优化调度方案。该方法实现了对随机DED模型各个场景和各个时段的解耦求解,将一个大规模优化问题分解为一系列的小规模优化问题,有效提高了对大电网随机DED模型的求解速度。以某一实际省级电网为算例,通过与场景法和鲁棒优化调度方法的比较验证了所提出模型和求解方法的正确有效性。     

A solution method using neural networks for the generator commitment problem

This paper studies the feasibility of applying the Hopfield-type neural network to unit commitment problems in a large power system. The unit commitment problem is to determine an optimal schedule of what thermal generation units must be started or shut off to meet the anticipated demand; it can be formulated as a complicated mixed integer programming problem with a number of equality and inequality constraints. In our approach, the neural network gives the on/off states of thermal units at each period and then the output power of each unit is adjusted to meet the total demand. Another feature of our approach is that an ad hoc neural network is installed to satisfy inequality constraints which take into account standby reserve constraints and minimum up/down time constraints. The proposed neural network approach has been applied to solve a generator scheduling problem involving 30 units and 24 time periods; results obtained were close to those obtained using the Lagrange relaxation method.     

一种用于机组组合问题的改进双重粒子群算法

为了更经济快速地解决机组组合问题,提出一种改进双重粒子群优化(particle swarm optimization,PSO)算法,包含离散部分和连续部分。离散PSO分时段优化机组的启停状态,在种群更新时加入了临界算子,改进了可行解的判别条件,各机组出力最低值的和要在一定程度上低于负荷需求值,并考虑机组启停时间的向前继承和向后约束。连续PSO用于启停状态确定过程中和确定后的负荷分配,考虑功率平衡约束、热备用约束和机组的出力上下限约束。求解经济负荷分配时,利用罚函数的方法满足机组的爬坡速率约束,最后得到煤耗最小值。采用2个24时段的算例进行仿真,实验结果表明新算法减少了搜索量,提高了收敛速度,并为机组组合问题提出了新思路。