Dispatch of direct load control using dynamic programming

An approach based on dynamic programming is presented for the dispatch of direct load control (DLC). The objective is to coordinate DLC strategies with system unit commitment such that the system production cost is minimized. To achieve this goal, the DLC dispatch is first integrated into the unit commitment problem. An optimization technique based on dynamic programming is then developed to reach the optimal DLC dispatch strategy and system generation schedule. To demonstrate the effectiveness of the approach, results from a sample study performed on the Taiwan power system are described     

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.     

Parallel micro genetic algorithm based on merit order loading solutions for constrained dynamic economic dispatch

This paper proposes a parallel micro genetic algorithm based on merit order loading solutions (PMGA-MOL) to solve constrained dynamic economic dispatch (DED) problems for combined cycle (CC) units with linear decreasing and decreasing staircase incremental cost (IC) functions. To minimize the synchronization overheads, the PMGA-MOL employs the load balancing and migration strategies among processors. This PMGA-MOL algorithm is implemented on the eight-processor scalable multicomputer implementation using low-cost equipment (SMILE) Beowulf cluster with a fast ethernet switch network on the generating unit system size in the range of 5–80 units over the entire dispatch periods. With different migration strategies, the proposed PMGA-MOL compromises the solution quality and speedup upper bounds for the best performance. PMGA-MOL is shown to be viable to the on-line implementation of constrained DED due to substantial generator fuel cost savings and high speedup upper bounds.     

Evolutionary programming based economic dispatch for units withnon-smooth fuel cost functions

This paper develops an efficient, general economic dispatch (ED) algorithm for generating units with nonsmooth fuel cost functions. Based on the evolutionary programming (EP) technique, the new algorithm is capable of determining the global or near global optimal dispatch solutions in the cases where the classical Lagrangian based algorithms cease to be applicable. Effectiveness of the new algorithm is demonstrated on two example power systems and compared to that of the dynamic programming, simulated annealing, and genetic algorithms. Practical application of the developed algorithm is additionally verified on the Taiwan power (Taipower) system. Numerical results show that the proposed EP based ED algorithm can provide accurate dispatch solutions within reasonable time for any type of fuel cost functions     

基于机会约束规划的直接负荷控制及可中断负荷联合优化调度研究

为充分利用需求响应资源,可对不同需求响应资源进行整合。本文以调度成本最低为目标函数,构建了含直接负荷控制和可中断负荷的优化模型。对比了直接负荷控制及可中断负荷在受控量、受控时间、补偿价格等方面的异同,重点分析了两者在负荷反弹方面的差异。采用机会约束考虑了负荷预测的不确定性,并将机会约束转化为其确定性等价形式。采用拉格朗日松弛法对确定性模型求解,并采用蒙特卡罗模拟对机会约束置信水平进行验证。算例表明模型综合了直接负荷控制移峰和可中断负荷削峰特点,可有效降低系统高峰时段负荷,避免二次负荷高峰的产生。     

A nonlinear fractional programming approach for environmental–economic power dispatch

A nonlinear fractional programming approach is provided for addressing the environmental–economic power dispatch problems in the thermal power dispatch systems. The objective of this study is to simultaneously minimize the total fuel cost and total emissions of the power dispatch systems, which is realized by two simultaneous models with nonlinear constraints. The first model is to minimize the quotient of two competing and conflicting functions (i.e. [total emission function]/[total fuel cost function]), and the second one is to minimize the total fuel cost expressed by a quadratic objective function. In particular, the process of solving the first model uses Dinkelbach’s algorithm to convert the minimization problem with the nonlinear fractional objective function into a sequence of non-fractional minimization problems. The effectiveness of this approach is demonstrated through applying to the standard IEEE 30-bus test system. Comparison between the present approach and other existing approaches shows that the proposed approach can generate superior decision alternatives from the view point of realizing a more environmentally friendly and cost-effective scheme and/or considering the power transmission loss rate in the power dispatch systems.     

Quasi-static economic dispatch using dynamic programming with an improved zoom feature

A quasi-static economic dispatch method is presented based on dynamic programming (DP) employing an improved zoom feature (DPZF). The DPZF method yields significant savings in computation time and memory compared with traditional DP methods, exhibiting a speed-up ratio of approximately 25:1. Other benefits of the DPZF method include no restrictions on the ‘shape’ (i.e., monotonic characteristic) of the incremental fuel cost curves, ease of incorporating forbidden operating regions of unit output, and ease of incorporating penalty factors for representing the effects of transmission losses on dispatch. In the context of this paper, the application of DPZF is directed solely towards providing the initial solution for a dynamic economic dispatch (DED) method. However, DPZF is also useful as a static base point economic dispatch calculation for real-time AGC.     

Air conditioner direct load control by multi-pass dynamicprogramming

The dispatch of air conditioner direct load control (DLC) using multi-pass dynamic programming (MPDP) methods is presented. The objective of this work is to schedule the control of air conditioner load by MPDP methods such that the peak load reduction and production cost saving have optimum results for the whole study period. The algorithm can quickly converge to an optimal schedule. To demonstrate the effectiveness of this approach, results of a sample study on the Taiwan Power Company power system are described in this paper     

一种求解电力经济负荷分配问题的改进微分进化算法

针对电力系统经济负荷分配(economic dispatch,ED)这一典型的非凸、非线性、组合优化问题,提出一种改进的微分进化(improved differential evolution,IDE)算法。微分进化(differential evolution,DE)算法虽有简单、搜索效率高的优点,但是仍然有局部最优的问题。该文在对DE算法搜索机理进行分析的基础上,针对DE算法参数难于动态调整的问题,提出不依赖于优化问题的控制参数自适应调整机制,并根据动态监视群体适应度方差的变化,增加个体迁移策略,进一步提高DE算法的全局寻优能力和鲁棒性。运用该算法对IEEE3机、40机及69机300节点标准测试用例进行计算,并考虑机组的爬坡约束、出力限制区约束、非光滑费用函数曲线等非线性特性,将其计算结果与遗传算法(genetic algorithm,GA)及粒子群算法(particle swarm optimization,PSO)进行比较,分析表明该方法是可行的、有效的。     

计及风险系数的含风电场电力系统多目标动态优化调度

随着风电并网容量的不断增加,传统的确定性优化调度方法已难以满足电力系统安全运行要求。本文建立了计及风险系数的含风电场电力系统多目标动态优化调度模型,模型包括风险系数、燃料成本及污染排放量最小3个目标,将风电场出力及负荷的不确定性纳入模型综合考虑。为了对模型中的随机变量进行处理,引入概率性序列理论,并对其运算空间进行扩展,然后提出了一种改进的多目标教与学优化算法对模型进行求解。含风电场的10机系统算例验证了本文模型及算法的可行性和有效性。     

考虑环境污染的机组出力经济分配

对传统意义下经济调度模型进行修正,同时考虑最小化燃料费用和污染排放量,提出了多目标环境经济调度模型,并应用多目标蚁群算法(MOACA)加以求解。指出MOACA将信息素交流和基于全局最优经验指导两种寻优方式相结合,以指导蚂蚁向更好解的方向前进,可以获得分布良好的Pareto最优解。利用文内算法对IEEE-30节点系统的机组出力进行环境经济调度,并与现有一些算法进行比较。     

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.     

电力市场下计及节能环保的实时发电调度策略

研究了电力市场环境下电网公司购电费用最小和煤耗(排放)最小双目标下实时调度策略问题.根据当前电力市场运营规则及实时调度自身特点与要求,在不影响计算精度的前提下简化了模型的复杂度,将2种不同优化目标下的最优策略应用反比例分配原则并结合相应的权重系数统一到一个模型与算式中,再利用优化排队法将所需调整的功率偏差量分配到相应机组.通过IEEE 3机9节点系统进行了仿真计算,验证了该模型算法的实用性和有效性.该算法所需数据少,计算量小,适合在电力市场条件下,运行方式调整频繁时快速得到计及购电费用及煤耗(排放)双目标的实时调度功率分配方案.     

Regional Approaches to Measurement and Verification of Load Management Programs

Conventional measurement and verification for non-interval metered, direct load control (DLC) programs bidding into wholesale electricity markets usually requires a PURPA-compliant load research study. This requirement contributes to high operating costs and has been a factor in recent reductions in the amount of emergency demand response available to regional transmission system operators. This paper describes a collaborative effort by PJM members to determine whether regional modeling using pooled historical data could satisfy DLC measurement and verification (M&V) requirements without sacrificing estimation accuracy. This paper also describes how PJM incorporated the regional "deemed savings estimates" into its Load Data Systems Manual. This paper concludes that regional approaches to M&V could yield large cost savings for DLC resource providers around the country.     

A Lexicographic Optimization and Augmented ϵ-constraint Technique for Short-term Environmental/Economic Combined Heat and Power Scheduling

Abstract—In recent years, combined heat and power units have become significant elements in conventional power stations due their numerous merits, including operational cost savings and reduced emissions. In this regard, this article proposes a short-term multi-objective framework for the combined heat and power economic/emission dispatch problem. In addition, to more precisely model the problem, the non-linear forms of fuel cost functions and valve-point loading along with power transmission loss are considered. The objectives of the problem are total cost minimization as well as minimization of pollutant emissions; lexicographic optimization and the augmented epsilon-constraint technique are employed to solve the multi-objective problem. Also, a fuzzy decision making technique has been used to select the most preferred solution among the Pareto solutions. Afterward, a comprehensive comparison is performed between the results obtained from the proposed method and those derived from the non-dominated sorting genetic algorithm II, strength Pareto evolutionary algorithm 2, and multi-objective line-up competition algorithm, verifying the superiority of the presented approach for lower execution time, total cost, and emission. Furthermore, the proposed model is implemented on a large-scale test system while the execution time is rational.     

A recursive economic dispatch algorithm for assessing the costs ofthermal generator schedules

The authors develop an efficient, recursive algorithm for determining the economic power dispatch of thermal generators within the unit commitment environment. The algorithm uses the equal incremental fuel cost criterion as its basis. In the algorithm, the fuel cost functions of the thermal generators are modeled by quadratic polynomials and the transmission losses are discounted. A method for incorporating the operation limits of the online generators and limits due to ramping generators is developed. The algorithm is amenable to computer implementation using the artificial intelligence programming language Prolog. The performance, of the algorithm was demonstrated through its application to the evaluation of the costs of dispatching 13 thermal generators within a generator schedule in a 24-h schedule horizon     

考虑需求响应虚拟机组和碳交易的含风电电力系统优化调度

在智能电网和低碳电力的背景下,提出一种考虑需求响应虚拟机组和碳交易的含风电电力系统优化调度模型。首先,将需求侧资源分为可调度资源和不可调度资源,在可调度资源中分别建立了价格需求响应虚拟机组和激励需求响应虚拟机组模型,并分析了两种虚拟机组的运行特点;其次,在优化调度模型中引入碳交易,并提出系统碳减排目标的概念及阶梯型碳排放权价格,分析其对碳排放量的制约情况。在此基础上,引入功率平衡约束、机组出力及爬坡约束、虚拟机组运行约束等,建立了以碳交易成本、火电机组发电成本和虚拟机组运行成本为目标的新型低碳经济调度模型,采用细菌群体趋药性(BCC)算法对模型进行求解。通过仿真算例对不同场景下系统的风电消纳情况和系统的综合运行成本进行了分析。算例结果验证了模型及求解方法的可行性及优越性。     

考虑综合需求侧响应的区域综合能源系统多目标优化调度

为兼顾区域综合能源系统（regional integrated energy system,RIES）中能耗成本、污染排放、风电消纳等多个调度目标,建立了考虑综合需求响应的RIES多目标优化模型。首先,对含电转气、储能系统、热电联产机组等设备的RIES建模,并在区域内引入了具体考虑削减负荷、转移负荷和替代负荷的综合需求响应,旨在削减系统负荷峰谷差。然后,分别建立了以系统用能成本、弃风功率和污染物治理成本最小的目标函数,采用多目标优化方法--以模糊加权规划遍历权值求解帕累托前沿,再根据证据推理决策方法寻找最优调度策略。最后基于典型算例研究,结果表明了所提多目标优化算法能有效在多个调度目标间做出权衡,考虑综合需求响应的RIES在总能耗、环境友好和风电消纳等方面更具优势。     

空间耦合粒子群优化算法及峰谷电价下IES-CCHP区域联合调度

综合能源系统中电力、天然气和热力系统之间的交互影响具有一定的相关性。考虑能源间转换关系以及系统对分时电价的响应,以最小化购售电计划交易成本、燃料成本和排放污染气体所产生的环境成本为目标,建立峰谷电价下冷热电联供(CCHP)系统区域联合环保经济调度模型。为解决粒子群优化算法求解模型时存在的优化效率低、易陷入局部最优、计算结果随机性强等问题,提出一种空间耦合粒子群优化算法。在粒子寻优多维参数空间上,通过引入耦合协调数学模型将各维参数有效耦合,从而使所有参数从总体上同时趋向最优解。仿真结果表明,相比经典粒子群优化算法和改进粒子群优化算法,空间耦合粒子群优化算法有较强的全局搜索能力和更可靠的优化计算结果;所提CCHP系统的联合调度模型能有效促进能源的高效利用、电力的经济调度和节能减排。     

A new model for optimal generation scheduling of power system considering generation units availability

The objective of the short-term combined economic–environmental dispatch is to obtain the optimal power outputs of all generating units in the system given simultaneous minimization of the corresponding fuel cost and the release of gaseous pollutants in the environment. In this paper the classical model of the dynamic combined economic–environmental power dispatch is upgraded considering the availability of the generating units present in the system. The unavailability of power generation is defined as risk index and is considered to be a function of the generating units power level. An efficient multi-objective based genetic algorithm is applied for optimization purposes. Combined hydro-thermal power system is used as a case study system. The results show increase of the availability of power generation followed by small increase of the fuel cost and the gaseous emission.