A study of a unit commitment problem with transmission constraints

Unit commitment problem is an optimization problem to determine the start‐up and shut‐down schedule of thermal units while satisfying various constraints, for example, generation‐demand balance, unit minimum up/down time, system reserve, and so on. Since this problem involves a large number of 0–1 type variables that represent up/down status of the unit and continuous variables expressing generation output, it is a difficult combinatorial optimization problem to solve. The study at present concerns the method for requiring the suboptimum solution efficiently. Unit commitment method widely used solves the problem without consideration of voltage, reactive power, and transmission constraints. In this paper, we will propose a solution of unit commitment with voltage and transmission constraints, based on the unit decommitment procedure (UDP) method, heuristic method, and optimal power flow (OPF). In this method, initial unit status will be determined from random numbers and the feasibility will be checked for minimum start‐up/shut‐down time and demand‐generation balance. If the solution is infeasible, the initial solution will be regenerated until a feasible solution can be found. Next, OPF is applied for each time period with the temporary unit status. Then, the units that have less contribution to the cost are detected and will be shut down based on the unit decommitment rules. This process will be repeated until suboptimal solution is obtained. The proposed method has been applied to the IEEE 118‐bus test system with 36 generating units with successful result. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 144(3): 36–45, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10187     

Thermal power generation scheduling by simulated competition

This paper presents a new method for solving the unit commitment problem by simulation of a competitive market where power is traded through a power exchange (PX). Procedures for bidding and market clearing are described. The market clearing process handles the spinning reserve requirements and power balance simultaneously. The method is used on a standard unit commitment problem with minimum up/down times, start-up costs and spinning reserve requirement taken into account. Comparisons with solutions provided by Lagrangian relaxation, genetic algorithms and Chao-an Li's unit decommitment procedure demonstrate the potential benefits of this new method. The motivation for this work was to design a competitive electricity market suitable for thermal generation scheduling. However, performance in simulations of the proposed market has been so good that it is presented here as a solving technique for the unit commitment problem     

Multi-Area Power Generation Dispatch in Competitive Markets

In competitive electric energy markets, the power generation dispatch optimization is one of the most important missions among generation companies-how to respond to the markets, dispatch their units, and maximize profits. This paper proposes an approach to incorporate power contracts, which include call and put options, forward contracts, and reliability must-run contracts, into multi-area unit commitment and economic dispatch solutions. The proposed solution algorithm is based on adaptive Lagrangian relaxation, unit decommitment, and lambda-iteration methods. The problem formulation consists of three stages: 1) the incorporation of the power contracts, 2) the multi-area unit commitment, and 3) the multi-area economic dispatch. The proposed algorithm has been successfully implemented, and its testing results on modified IEEE test cases are promising.     

基于改进拉格朗日乘子修正方法的逆序排序机组组合

机组组合与经济调度是两个不同范畴的优化决策问题,其优化过程在概念上有本质的区别。用经济调度中的拉格朗日乘子对机组组合中的乘子进行修正有概念含混的误区。文章在阐明机组组合与经济调度中拉格朗日乘子的差异及作用机理的基础上,提出了一种新的逆序排序机组组合中拉格朗日乘子的修正方法,并对机组的搜索范围及机组运行的经济指标作了相应的改进,使原有算法在精度和计算速度上均得到了显著提高。20机、26机及110机测试系统的计算结果表明了文中的改进方法是有效的,进一步增强了机组组合对大规模系统的适应性。     

Unit commitment in interconnected generating systems using aprobabilistic technique

A probabilistic technique is presented which can be used to develop unit commitment schedules for continually changing loads in an interconnected power system configuration for a specified period. The technique is developed on the basis of each area in a multi-area configuration fulfilling one of two different risk criteria. This approach, which is known as the two-risks concept, was illustrated in a recent publication (R. Billinton and N.A. Chowdhury, see ibid., vol.3, p.1479-87, 1988). The unit commitment during a specified scheduling period is constrained by risk criteria and economic factors. Typical unit commitment cases are illustrated with numerical examples     

Application of genetic-based neural networks to thermal unitcommitment

A new approach using genetic algorithms based neural networks and dynamic programming (GANN-DP) to solve power system unit commitment problems is proposed in this paper. A set of feasible generator commitment schedules is first formulated by genetic-enhanced neural networks. These pre-committed schedules are then optimized by the dynamic programming technique. By the proposed approach, learning stagnation is avoided. The neural network stability and accuracy are significantly increased. The computational performance of unit commitment in a power system is therefore highly improved. The proposed method has been tested on a practical Taiwan Power (Taipower) thermal system through the utility data. The results demonstrate the feasibility and practicality of this approach     

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

This paper presents a Hopfield artificial neural network for unit commitment and economic power dispatch. The dual problem of unit commitment and economic power dispatch is an example of a constrained mixed-integer combinatorial optimization. Because of uncertainties in both the system load demand and unit availability, the unit commitment and economic power dispatch problem is stochastic. In this paper we model forced unit outages as independent Markov processes, and load demand as a normal Gaussian random variable. The (0,1) unit commitment-status variables and the hourly unit loading are modelled as sample functions of appropriate random processes. The problem variables over which the optimization is done are modelled as sample functions of random processes which are described by Ito stochastic differential equations. The method is illustrated by a simple example of a power system having three machines which are committed and dispatched over a four-hour period. In the method, unit commitment and economic dispatch are done simultaneously.     

基于免疫算法的机组组合优化方法

机组组合是改善传统电力系统运行经济性和电力市场出清的重要手段。基于群体进化的智能优化算法存求解过程中存在计算效率低和易于早熟收敛等缺点。提出机组组合的免疫算法，利用免疫算法保持种群多样性的内在机制和免疫记忆特性改进既有的智能优化方法。新算法扩展了约束处理技术，能更好地对可行解空间搜索，采用一种由后向前、由前及后、双向迂回推进的精简程序改善个体可行解的局部最优性，同时利用优先级顺序法产生能较好反映问题先验知识的初始种群。典型算例证实新算法能获得更优的结果，具有更快的收敛速度，且在系统规模扩大时有大致线性的计算复杂性，是一种新的高效的机组组合智能优化算法。     

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。     

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.     

A parallel genetic algorithm approach to solving the unitcommitment problem: implementation on the transputer networks

Through a constraint handling technique, this paper proposes a parallel genetic algorithm (GA) approach to solving the thermal unit commitment (UC) problem. The developed algorithm is implemented on an eight-processor transputer network, processors of which are arranged in master-slave and dual-direction ring structures, respectively. The proposed approach has been tested on a 38-unit thermal power system over a 24-hour period. Speed-up and efficiency for each topology with different number of processor are compared to those of the sequential GA approach. The proposed topology of dual-direction ring is shown to be well amenable to parallel implementation of the GA for the UC problem     

大规模系统月度机组组合和安全校核算法

采用时序优化方式解决月度机组组合和电网安全校核问题,针对电力市场和节能调度模式,建立了优化数学模型。利用拉格朗日松弛算法进行月度720时段机组组合优化,利用非线性内点最优潮流算法进行电网安全校核。以IEEE RTS标准算例和中国华东电网为例进行大规模优化性能分析,结果表明该算法是解决大规模电力系统月度发电计划和电网安全校核的有效方法。     

考虑风电的电力系统机组组合两阶段优化方法

电的随机性和波动性给电力系统的安全经济运行带来了严峻的挑战,合理的风电不确定性模型及机组组合优化方法是保证电力系统日前调度安全性和经济性的关键。为此,提出一种考虑风电的电力系统机组组合两阶段随机优化方法。根据风电出力历史数据的非参数经验分布,生成符合风电随机性和波动性的风电动态场景。考虑到场景削减过程中容易忽略的一些极端边界场景会增加系统的弃风或切负荷风险,提出以削减后的场景和极端边界场景为输入的机组组合两阶段优化模型。同时,为求解机组组合这一非线性混合整数优化问题,提出一种混合遗传纵横交叉算法的优化方法。通过实验仿真结果证明了所提模型和方法用于求解考虑风电的电力系统机组组合问题时的合理性和有效性。     

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.     

A method for unit commitment with transmission losses and flow constraint

Researches on the unit commitment with transmission network have been reported recently. However, most of these researches mainly discussed the security constrained unit commitment, while the relationship between unit commitment and transmission losses was not considered. However, from the standpoint of operating reserve for ensuring power supply reliability, a unit commitment considering transmission losses is required. Further, under the deregulation and liberalization of the electric power industry, not only the line's security but also transmission losses are expected to play an important role in calculating the network access charge, and unit commitment taking into account transmission losses is also desired from this viewpoint. In this paper, a unit commitment approach with both transmission losses and line flow constraint is presented. Based on a heuristic iterative optimization method, first, an initial schedule is created by using a successively decommitting unit approach that is proposed in this paper. Then, we determine constraints included in the unit commitment schedule by a heuristic iterative optimization approach, in which an algorithm able to get rid of line overload by DC optimal power flow is developed. Through numerical simulations on two test power systems, the effectiveness of the proposed method is shown. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 142(4): 9–19, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10116     

Optimal generation scheduling with ramping costs

In this paper, a decomposition method is proposed which relates the unit ramping process to the cost of fatigue effect in the generation scheduling of thermal systems. The objective of this optimization problem is to minimize the system operation cost, which includes the fuel cost for generating the required electrical energy and starting up decommitted units, as well as the rotor depreciation during ramping processes, such as starting up, shutting down, loading, and unloading. According to the unit fatigue index curves provided by generator manufacturers, fixed unit ramping-rate limits, which have been used by previous studies, do not reflect the physical changes of generator rotors during the ramping processes due to the fatigue effect. By introducing ramping costs, the unit on/offstates can be determined more economically by the proposed method. The Lagrangian relaxation method is proposed for unit commitment and economic dispatch, in which the original problem is decomposed into several subproblems corresponding to the optimization process of individual units. The network model is employed to represent the dynamic process of searching for the optimal commitment and generation schedules of a unit over the entire study time span. The experimental results for a practical system demonstrate the effectiveness of the proposed approach in optimizing the power system generation schedule     

基于改进的逆序排序法的机组组合优化算法

文章提出了改进的逆序排序法来求解机组组合优化问题.该算法从可用机组全投入运行这一可行解出发,在每次迭代过程中优化一台机组在整个调度周期内的开停状况,以最小化总生产成本或总购电成本,直到连续两次迭代的目标函数值不再减小为止.该方法的显著优点在于计算不会振荡,迭代不会发散,且每次迭代的结果均为可行解.该算法在单机组优化过程中,以机组的最小启停区间而不是单个时段为研究调度对象,缓解了组合爆炸问题,明显地加快了计算速度.     

一种考虑网络损耗及线路过负荷的火力发电机起停计划方法

以面向实际应用为目的，提出了一种考虑输电网络损耗及线路过负荷约束的火力发电机起停计划方法。首先用动态规划法建立一个不含约束条件的初始解，然后运用启发式方法对初始解进行修正使之逐个满足各约束条件得到运行可能解，并通过修改各发电机的起动优先顺序使此过程反复进行直至得到（准）最佳解。在此过程中引入最优潮流计算考虑输电网络损耗及线路过负荷等网络因素对发电机起停计划的影响成为可能，并提出一种调节发电机出力和改变发电机起停计划相结合的消除线路过负荷的方法。在一个8机44母线的测试系统上对提案方法进行了各种条件下的试算，验证了所提出的方法对解决考虑网络因素影响的发电机起停计划问题有效性。计算结果还表明：不仅线路过负荷起停计划问题的有效性。计算结果还表明：不公线路过负荷约束，网络损耗也对发电机起停 计划有较大影响。     

Application embedded chaos search immune genetic algorithm for short-term unit commitment

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 shutdown 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 chaos search and the fuzzy system 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 IGA combined with the Chaos Search and FS was carried out. The results show that the Chaos Search and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

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.