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.     

Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.     

Solving unit commitment problems with general ramp constraints

Lagrangian relaxation (LR) algorithms are among the most successful approaches for solving large-scale hydro-thermal unit commitment (UC) problems; this is largely due to the fact that the single-unit commitment (1UC) problems resulting from the decomposition, incorporating many kinds of technical constraints such as minimum up- and down-time requirements and time-dependent startup costs, can be efficiently solved by dynamic programming (DP) techniques. Ramp constraints have historically eluded efficient exact DP approaches; however, this has recently changed [Frangioni A, Gentile C. Solving nonlinear single-unit commitment problems with ramping constraints. Oper Res 2006;54(4):767–75]. We show that the newly proposed DP algorithm for ramp-constrained (1UC) problems allows to extend existing LR approaches to ramp-constrained (UC); this is not obvious since the heuristic procedures typically used to recover a primal feasible solution are not easily extended to take ramp limits into account. However, dealing with ramp constraints in the subproblems turns out to be sufficient to provide the LR heuristic enough guidance to produce good feasible solutions even with no other modification of the approach; this is due to the fact that (sophisticated) LR algorithms to (UC) duly exploit the primal information computed by the Lagrangian Dual, which in the proposed approach is ramp feasible. We also show by computational experiments that the LR [approach] is competitive with those based on general-purpose mixed-integer program (MIP) solvers for large-scale instances, especially hydro-thermal ones.     

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。     

考虑多种约束条件的机组组合新算法

提出了考虑系统降出力备用约束、机组出力变化速率、线路潮流约束和断面传输功率约束的机组组合新算法。算法没有引入任何乘子,计算单调收敛,速度快,并且不需要初始可行解。用ＩＥＥＥ ２４母线系统对算法进行了验证,结果表明,算法对各种约束条件的处理正确,解的质量好。     

确定机组组合的一种改进的动态规划方法

提出了一种确定机组组合的改进动态规划方法,称为插值动态规划算法。这是一种启发式方法,可以和其他的经济调度算法相结合,用以解决多种约束条件下的机组组合问题,特别是可以处理机组功率上升、下降速度约束,且考虑了机组的开、停机特性、并有效避免了“维数灾”问题,经实践检验是一种简单、有效的实用算法。     

A Method for Solving the Fuel Constrained Unit Commitment Problem

The unit commitment problem involves finding the hourly commitment schedule for the thermal units of an electrical system, and their associated generation, over a period of up to a week. For some utilities, contractual or other factors limit the amount of fuel available to certain of the units or plants. This paper describes a new method which solves the unit commitment problem in the presence of fuel constraints. The method uses a Lagrangian decomposition and successive approximation technique for solving the unit commitment problem where the generation, reserve and fuel constraints are adjoined onto the cost function using Lagrange multipliers. All important operating constraints have been incorporated including minimum up and down times, standby operation, ramping limits, time-dependent start-up cost, spinning and supplemental reserve. The method is being applied to a production-grade program suitable for Energy Management Systems applications.     

Short-term resource scheduling with ramp constraints [powergeneration scheduling]

This paper describes a Lagrangian relaxation-based method to solve the short-term resource scheduling (STRS) problem with ramp constraints. Instead of discretizing the generation levels, the ramp rate constraints are relaxed with the system demand constraints using Lagrange multipliers. Three kinds of ramp constraints, startup, operating and shutdown ramp constraints are considered. The proposed method has been applied to solve the hydro-thermal generation scheduling problem at PG&E. An example alone with numerical results is also presented     

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.     

Using immune genetic algorithm based hybrid techniques for short-term unit commitment problem

This paper presents a hybrid chaos search (CS), immune algorithm (IA)/genetic algorithm (GA), and fuzzy system (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shut-down schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve, and individual units. First, we combined the IA and GA, then we added the CS and the FS approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20, and 30 thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), standard genetic algorithm (SGA), traditional simulated annealing (TSA), and traditional Tabu search (TTS). A comparison with an immune genetic algorithm (IGA) combined with the CS and FS was carried out. The results show that the CS and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

基于内点半定规划的机组组合问题

提出一种基于内点半定规划(semidefinite program- ming, SDP)直接求解机组组合(unit commitment, UC)问题的新方法。通过引入辅助变量,该方法将原整数变量约束转化为凸二次约束,进而将UC问题转化为半定规划问题,并用现代内点法进行求解。针对计算结果中整数变量存在微小偏差的问题,采用启发式技术进行修正。100机24时段等6个系统的仿真结果表明,所提方法能有效处理机组爬坡约束,具有较快的计算时间,适合于求解大规模的UC问题,是一种有应用前景的方法。     

具有爬升约束机组组合的充分必要条件

在Lagrangian松弛框架下，很难确定机组组合问题的一个可行解是否可通过调整对偶机组组合而获得。对于具有爬升约束的机组组合调度问题来说，由于机组出力在连续的2个开机区间的耦合性，求解可行解就更困难。在Lagrangian松弛框架下，开发1个机组组合新方法的核心是如何获得1个可行的机组组合。文中采用Benders分解可行性条件严格证明了在给定时段，机组组合可行的充分必要条件：即在该时段一个相应于系统负载平衡约束和旋转各用约束的不等式组成立。该条件不需要求解经济分配问题，就可以判定机组组合的可行性。有了此条件，可在发电功率经济分配前知道机组组合是否可行，若不可行，则可通过调整机组组合状态而获得可行的组合。该条件对于构造一个求解机组组合问题的系统方法是重要且有效的。数值测试表明该条件是判定机组组合可行性的有效方法。     

A new approach to security-constrained generation scheduling of large-scale power systems with a piecewise linear ramping model

This paper presents a new and efficient approach to determine security-constrained generation scheduling (SCGS) in large-scale power systems, taking into account dispatch, network, and security constraints in pre and post-contingency states. A novel ramp rate limit is also modeled as a piecewise linear function in the SCGS problem to reflect more practical characteristics of the generating units. Benders decomposition is applied to this constrained solution process to obtain an optimal SCGS problem based on mixed-integer nonlinear programming (MINLP). The formulation can be embedded in two stages. First, a MIP is formulated in the master problem to solve a unit commitment (UC) problem. This stage determines appropriate on/off states of the units. The second stage, the subproblem, is formulated as a NLP to solve a security-constrained economic dispatch (SCED) problem. This stage is used to determine the feasibility of the master problem solution. It provides information to formulate the benders cuts that connect both problems. The proposed approach is tested in the IEEE 118-bus system to show its effectiveness. The simulation results are more realistic and feasible, whilst assuring an acceptable computation time.     

Implementation of a Lagrangian relaxation based unit commitmentproblem

An effort is made to provide an understanding of the practical aspects of the Lagrangian relaxation methodology for solving the thermal unit commitment problem. Unit commitment is a complex, mixed integer, nonlinear programming problem complicated by a small set of side constraints. Until recently, unit commitment for realistic size system has been solved using heuristic approaches. The Lagrangian relaxation offers a new approach for solving such problems. Essentially, the method involves decomposition of the problem into a sequence of master problems and easy subproblems, whose solutions converge to an ϵ-optimal solution to the original problem. The authors concentrate on the implementation aspects of the Lagrangian relaxation method applied to realistic and practical unit commitment problems     

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。     

Unit Commitment solution using an optimized genetic system

This paper presents an investigation into the application of an optimized Genetic Algorithm (GA) to solve the Thermal Unit Commitment (UC) problem. A Parallel structure was first developed to handle the infeasibility problem in a structured and improved GA which provides an effective search process and therefore greater economy. The proposed methodology resulted in a better performance with faster operation by using both computational methods and classification of unit characteristics. Typical constraints such as system power balance, minimum up and down times, start-up and shut-down ramps, have also been considered. A number of important parameters (standard and new parameters) of the UC problem have been identified. The proposed method is implemented and tested using a C# program. The tests are carried out using two systems including 10 and 20 units during a scheduling period of 24 h. The results are finally compared with those obtained from genetic schemes in other similar investigations through which the effectiveness of the proposed scheme is affirmed.     

A matrix real-coded genetic algorithm to the unit commitment problem

An approach to solving the unit commitment (UC) problem is presented based on a matrix real-coded genetic algorithm (MRCGA) with new repairing mechanism and window mutation. The MRCGA chromosome consists of a real number matrix representing the generation schedule. Using the proposed coding, the MRCGA can solve the UC problem through genetic operations and avoid coping with a suboptimal economic dispatch (ED) problem. The new repairing mechanism guarantees that the generation schedule satisfies system and unit constraints. The window mutation improves the MRCGA searching performance. Numerical results show an improvement in the solution cost compared with the results obtained from other algorithms.     

A dynamic programming based fast computation Hopfield neural network for unit commitment and economic dispatch

This paper develops a new dynamic programming based direct computation Hopfield method for solving short term unit commitment (UC) problems of thermal generators. The proposed two step process uses a direct computation Hopfield neural network to generate economic dispatch (ED). Then using dynamic programming (DP) the generator schedule is produced. The method employs a linear input–output model for neurons. Formulations for solving the UC problems are explored. Through the application of these formulations, direct computation instead of iterations for solving the problems becomes possible. However, it has been found that the UC problem cannot be tackled accurately within the framework of the conventional Hopfield network. Unlike the usual Hopfield methods which select the weighting factors of the energy function by trials, the proposed method determines the corresponding factor using formulation calculation. Hence, it is relatively easy to apply the proposed method. The Neyveli Thermal Power Station (NTPS) unit II in India with three units having prohibited operating zone has been considered as a case study and extensive study has also been performed for power system consisting of 10 generating units.     

多区域输电阻塞管理的拉格朗日松驰分解算法

提出一种新的基于增广拉格朗日松驰的区域分解最优潮流算法,将一个大的最优潮流问题分解成多个区域子问题,并用此算法求解多区域电力市场输电阻塞管理问题,与现有的其他方法相比,该算法的主要优点在于无需在原始网络模型的基础上增加任何虚拟发电机或负荷,通过将该算法与电力市场实时平衡机制相结合,多区域有力阻塞管理问题可以分解为单区域二次规划子问题。这些子问题可以顺序求解也可以并行求解。采用这一方法,所有的区域市场独立调度员在得到不到其他区域网络信息的情况下仍然可以相互协作消除网络阻塞,在这一过程中,惟一需要进行区域间交换的信息是与区域间“耦合”约束相对应的拉格朗日乘子,最后,通过分析3区域的IEEE RTS－96标准测试系统说明了该方法的有效性。     

Effects of ramp-rate limits on unit commitment and economicdispatch

The authors propose an algorithm to consider the ramp characteristics in starting up and shutting down the generating units as well as increasing and decreasing power generation. They consider the inclusion of ramping constraints in both unit commitment and economic dispatch. Since implementing ramp-rate constraints is a dynamic process, dynamic programming (DP) is a proper tool to treat this problem. To overcome the computational expense which is the main drawback of DP, this study initially employs artificial intelligence techniques to produce a unit commitment schedule which satisfies all system and unit operation constraints except unit ramp-rate limits. Then, a dynamic procedure is used to consider the ramp properties as units are started up and shut down. According to this adjustment, maximum generating capabilities of units will change the unit operation status instead of following a step function. Finally, a dynamic dispatch procedure is adopted to obtain a suitable power allocation which incorporates the unit generating capability information given by unit commitment and unit ramping constraints, as well as the economical considerations. Two examples are presented to demonstrate the efficiency of the method