Unit commitment using a hybrid model between Lagrangian relaxation and genetic algorithm in competitive electricity markets

This paper presents a hybrid model between Lagrangian relaxation (LR) and genetic algorithm (GA) to solve the unit commitment problem. GA is used to update the Lagrangian multipliers. The optimal bidding curves as a function of generation schedule are also derived. An IEEE 118-bus system is used to demonstrate the effectiveness of the proposed hybrid model. Simulation results are compared with those obtained from traditional unit commitment.     

A combination of the genetic algorithm and lagrangian relaxation decomposition techniques for the generation unit commitment problem

Unit commitment involves the scheduling of generators in a power system in order to meet the requirements of a given load profile. An analysis of the basis for combining the genetic algorithm (GA) and Lagrangian relaxation (LR) methods for the unit commitment problem is presented. It is shown that a robust unit commitment algorithm can be obtained by combining the global search property of the genetic algorithm with the ability of the Lagrangian decomposition technique to handle all kinds of constraints such as pollution, unit ramping and transmission security.     

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.     

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.     

Short-term thermal generation scheduling using improved immune algorithm

This paper proposes a new immune algorithm (NIA), which merges the fuzzy system (FS), the annealing immune (AI) method and the immune algorithm (IA) together, to resolve short-term thermal generation unit commitment (UC) problems. This proposed method differs from its counterparts in three main aspects, namely: (1) changing the crossover and mutation ratios from a fixed value to a variable value determined by the fuzzy system method, (2) using the memory cell and (3) adding the annealing immune operator. With these modifications, we can attain three major advantages with the NIA, i.e. (1) the NIA will not fall into a local optimal solution trap; (2) the NIA can quickly and correctly find a full set of global optimal solutions and (3) the NIA can achieve the most economic solution for unit commitment with ease. The UC determines the start-up and shut-down schedules for related generation units to meet the forecasted demand at a minimum cost while satisfying other constraints, such as each unit's generating limit. The NIA is applied to six cases with various numbers of thermal generation units over a 24-h period. The schedule generated by the NIA is compared with that by several other methods, including the dynamic programming (DP), the Lagrangian relaxation (LR), the standard genetic algorithm (GA), the traditional simulated annealing (SA) and the traditional Tabu search (TS). The comparisons verify the validity and superiority in accuracy for the proposed method.     

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.     

Economic Consequences of Alternative Solution Methods for Centralized Unit Commitment in Day-Ahead Electricity Markets

Many wholesale electricity markets call on the independent system operator (ISO) to determine day-ahead schedules for generators based on a centralized unit commitment. Up until recently, the Lagrangian relaxation (LR) algorithm was the only practical means of solving an ISO-scale unit commitment problem, and it was the solution technique used by most ISOs. Johnson et al. [1] demonstrate, however, that equity, incentive, and efficiency issues will arise from use of LR solutions, because different commitments that are similar in terms of total system costs can result in different surpluses to individual units. Recent advances in computing capabilities and optimization algorithms now make solution of the mixed-integer programming (MIP) formulation by means of branch and bound (B&B) tractable, often with optimality gaps smaller than those of LR algorithms, which has led some ISOs to adopt B&B algorithms and others proposing to do so. With the move towards B&B, one obvious question is whether the use of MIP will eliminate or reduce the issues with LR raised by Johnson et al. Using actual market data from an ISO, we demonstrate that both LR and MIP solutions will suffer the same equity issues, unless the ISO unit commitment problems can be solved to complete optimality within the allotted timeframe-which is beyond current computational capabilities. Our results further demonstrate that the size of the payoff deviations are not monotone in the size of the optimality gap, meaning smaller optimality gaps from B&B will not necessarily mitigate the issues Johnson et al. raise. We show that the use of "make-whole" payments, which ensure units recover any startup and no-load costs not recovered by inframarginal energy rents, can help to reduce surplus volatility and differences to some extent.     

A new unit commitment method

This paper introduces a new unit commitment method based on a decommitment procedure for solving the power system resource scheduling problem. From an initial schedule of all available units committed over the study period, a `one-at-a-time' unit decommitment is accomplished by dynamic programming according to some specified economic criteria. The decommitment process continues until no further reduction in total cost is possible, or the unit schedules of two consecutive iterations over the time period remain unchanged without any violation of the spinning reserve constraint. Two criteria for decommiting a unit are introduced and described in detail. Comparisons of the proposed unit commitment method with the Lagrangian relaxation (LR) approach and Fred Lee's sequential unit commitment method (SUC) demonstrate the potential benefits of the proposed approach for power system operations planning     

A genetic algorithm solution to the unit commitment problem

This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported     

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.     

A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming

This paper proposes an approach which combines Lagrangian relaxation principle and evolutionary programming for short-term thermal unit commitment. Unit commitment is a complex combinatorial optimization problem which is difficult to be solved for large-scale power systems. Up to now, the Lagrangian relaxation is considered the best to deal with large-scale unit commitment although it cannot guarantee the optimal solution. In this paper, an evolutionary programming algorithm is used to improve a solution obtained by the Lagrangian relaxation method: Lagrangian relaxation gives the starting point for a evolutionary programming procedure. The proposed algorithm takes the advantages of both methods and therefore it can search a better solution within short computation time. Numerical simulations have been carried out on two test systems of 30 and 90 thermal units power systems over a 24-hour periods.     

适用于不同电价机制的统一机组组合算法

现有电力市场中存在两种结算电价机制：按机组报价结算(一机一价)和按市场出清价格结算(统一电价)。不同市场之间的结算方式也有所不同,例如,双边交易中采用一机一价结算方式,而实时市场中采用边际电价结算方式。不同结算电价机制下,机组组合的目标函数不同,传统机组组合方法必须根据电价机制的不同进行调整。通过研究发现,两种结算方式下机组组合问题的最优条件具有类似的数学表达形式。基于这一统一的最优条件表达形式,提出了一种新的机组组合算法。与传统拉格朗日松弛法相比,新算法能够有效地求解两种电价机制下的机组组合问题。     

基于自适应系统优化算法的机组组合

算法采用系统分解理论将系统约束松弛,把机组组合问题分解为2层优化问题.上层通过拉格朗日乘子的自适应调整来协调单个机组的子系统,下层采用遗传算法求解单个机组独立的子系统优化问题.对拉格朗日乘子的自适应调整明显减少了对偶间隙的振荡现象,对遗传算法中交叉变异算子自适应的调整有效地克服了早熟现象.算例表明可行解的质量高、收敛速度快,与传统算法相比具有更高的自适应性,适用于大规模、复杂系统的机组组合问题的求解.     

一种求解大规模机组组合问题的混合智能遗传算法

针对传统的采用二进制编码的遗传算法在求解大规模机组组合问题时收敛速度慢、易早熟等问题,作者结合机组组合问题的特点,提出了一种混合智能遗传算法.该算法以机组状态作为个体编码,结合启发式方法的自适应智能变异算子求解目标函数,显著缩小了求解问题的规模,保证了群体多样性,提高了算法的搜索效率,改善了算法的收敛性.仿真计算结果表明了该算法的有效性和实用性.     

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。     

用于机组优化组合的改进单亲遗传算法

为了有效地解决火电厂机组优化组合问题,作提出了一种改进的单亲遗传算法。该算法使用实数编码,不使用在两条染色体之间操作的交叉算子,所有遗传操作全部在一条染色体上进行,简化了遗传操作过程,提高了计算效率,且不要求初始群体中的个体具有多样性,也不存在“早熟”收敛现象。与传统的机组优化组合方法相比,该方法能方便地处理机组优化组合问题的复杂约束条。计算实例验证了这种算法的有效性。     

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。     

Bidding information to generate bidding strategies for LaGrangian relaxation-based auctions

LaGrangian relaxation (LR) is used as an auction method for bidding in a deregulated environment. Identical or similar units can prevent LR from finding the optimal solution when only one of the units should be committed. If many units are similar, LR may have trouble selecting some subset of them for the optimal solution. A unique feasible solution may thus not be found. This leads to inequity among the unit(s) not selected and may result in less revenue for one or more competitors. Because the dispatcher has to use heuristic selection, there is no ‘fair’ solution to these problems. This paper focuses on how to change unit data to obtain an advantage while using LR as an auction method. The authors suggest alternative strategies based on previously published problems with selection by unit commitment and subsequent dispatch by economics. Sensitivity analysis results demonstrate the method for finding the percentage difference between units to affect the solution.     

遗传/禁忌组合算法在发电机组优化组合中的应用

在研究遗传算法 (GA)和禁忌算法 (TS)的基础上 ,提出一种采用遗传 /禁忌组合算法 (GA/TS)的策略 ,并将其应用于发电机组的优化组合中 ,同时用算例证明该方法的有效性和应用前景。     

基于混沌遗传混合优化算法的短期负荷环境和经济调度

环境和经济短期负荷调度主要由在调度周期内的最优机组组合和负荷分配组成,该文将优先次序法、遗传算法与混沌优化相结合,以应用到电站机组环境／经济运行优化问题中,在混沌遗传算法中采用递阶基因结构,将控制基因用于机组组合全局粗寻优,参数基因用于负荷分配局部优化, 基因修正与罚函数相结合解决约束问题,采用混沌扰动避免遗传算法早熟,运用基于线性搜索的混沌局部优化方法,加快算法的收敛速度和降低计算时间,优化计算结果可以同时得到最优机组组合及负荷最优分配,为实际调度系统提供了一个良好的方法。