Cost/environmentally compromised dispatch for cascaded hydrothermal system using artificial bee colony algorithm

This paper evaluates the robustness of the artificial bee colony (ABC) algorithm while allocating optimal power generation in a hydrothermal power system at the level of minimum fuel cost and minimum pollutant emission impacts on the environment subjected to physical and technical constraints. The hydrothermal scheduling (HTS) is devised in a bi‐objective framework so as to optimize both objectives of fuel cost and emission release, individually and simultaneously subjected to a verity of intricate equality and inequality constraints. Initially, all feasible solutions are obtained through random search, and then the ABC algorithm is used for the exploration and exploitation processes together in the search space, thereby discovering the optimal hourly schedule of power generation in the hydrothermal system. Meanwhile, a dependent hydro‐discharge computation handles the equality constraints; especially, the reservoir end volume and slack thermal generating unit for each sub‐interval handle the power balance equality constraint. The performance of the proposed approach is illustrated on a multi‐chain interconnected hydrothermal power system with due consideration of the water transport delay between connected reservoirs and transmission loss of system load. The results obtained from the proposed technique are compared with those of other techniques. The results demonstrate that the ABC algorithm is feasible and efficient for solving the HTS problem. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

A solution to the unit commitment problem considering LNG fuel constraints

In this paper, an algorithm is proposed for finding a quasi-optimal schedule for the short-term thermal unit commitment problem taking LNG fuel constraints into account. In recent years, LNG fuel has been used increasingly. As a result, LNG fuel constraints should be considered in making a unit commitment schedule. Generally, unit commitment is a nonlinear combinatorial problem including discrete variables. To solve the problem, a two-step algorithm is developed using mathematical programming methods. First a linear programming problem is solved to determine the amount of LNG fuel to be consumed by each LNG unit, then a Lagrangian relaxation approach is used to obtain a unit commitment schedule. This two-step algorithm simplifies the problem and thus has good convergence characteristics. To test the effectiveness of the proposed algorithm, a numerical simulation was carried out on a 46-unit thermal system over a 24-hour period. A result with a dual gap of 0.00546 was obtained. © 1998 Scripta Technica, Electr Eng Jpn, 125(3): 22–30, 1998     

Efficient real coded genetic algorithm to solve the non-convex hydrothermal scheduling problem

A simple and efficient optimisation procedure based on real coded genetic algorithm is proposed for the solution of short-term hydrothermal scheduling problem with continuous and non-smooth/non-convex cost function. The constraints like load-generation balance, unit generation limits, reservoir flow balance, reservoir physical limitations and reservoir coupling are also considered. The effectiveness of the proposed algorithm is demonstrated on a multichain-cascaded hydrothermal system that uses non-linear hydro generation function, includes water travel times between the linked reservoirs, and considers the valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint-handling technique, which eliminates the need for penalty parameters. A simple strategy based on allowing infeasible solutions to remain in the population is used to maintain diversity. The same problem is also solved using binary coded genetic algorithm. The features of both algorithms are same except the crossover and mutation operators. In real coded genetic algorithm, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in binary coded genetic algorithm. The comparison of the two genetic algorithms reveals that real coded genetic algorithm is more efficient in terms of thermal cost minimisation for a short-term hydrothermal scheduling problem with continuous search space.     

基于网损因子迭代的安全约束机组组合算法

针对考虑安全约束的机组组合(security constrained unit commitment,SCUC)问题,在传统SCUC模型的基础上,建立考虑有功网损及其在电网中分布的SCUC模型,提出一种基于网损因子迭代的SCUC算法。此算法每次迭代先解固定网损因子的SCUC问题,求得机组的运行状态,然后进行交流潮流计算,更新网损因子,进入下一次迭代。针对可能出现的网损因子振荡问题,提出SCUC和经济调度相结合的方法,选择对应发电成本较小的机组启停状态,进行经济调度优化和网损因子迭代计算,直至算法收敛。对IEEE 30和IEEE 118节点系统进行的仿真计算验证了所提算法的正确性和有效性。     

A new genetic-based tabu search algorithm for unit commitment problem

This paper presents a new algorithm based on integrating the use of genetic algorithms and tabu search methods to solve the unit commitment problem. The proposed algorithm, which is mainly based on genetic algorithms incorporates tabu search method to generate new population members in the reproduction phase of the genetic algorithm. In the proposed algorithm, genetic algorithm solution is coded as a mix between binary and decimal representation. A fitness function is constructed from the total operating cost of the generating units without penalty terms. In the tabu search part of the algorithm, a simple short term memory procedure is used to counter the danger of entrapment at a local optimum by preventing cycling of solutions, and the premature convergence of the genetic algorithm. A significant improvement of the proposed algorithm results, over those obtained by either genetic algorithm or tabu search, has been achieved. Numerical examples also showed the superiority of the proposed algorithm compared with two classical methods in the literature.     

Artificial bee colony algorithm for solving multi-objective optimal power flow problem

This paper presents a new and efficient method for solving optimal power flow (OPF) problem in electric power systems. In the proposed approach, artificial bee colony (ABC) algorithm is employed as the main optimizer for optimal adjustments of the power system control variables of the OPF problem. The control variables involve both continuous and discrete variables. Different objective functions such as convex and non-convex fuel costs, total active power loss, voltage profile improvement, voltage stability enhancement and total emission cost are chosen for this highly constrained nonlinear non-convex optimization problem. The validity and effectiveness of the proposed method is tested with the IEEE 9-bus system, IEEE 30-bus system and IEEE 57-bus system, and the test results are compared with the results found by other heuristic methods reported in the literature recently. The simulation results obtained show that the proposed ABC algorithm provides accurate solutions for any type of the objective functions.     

Optimal reactive power dispatch using self-adaptive real coded genetic algorithm

In this paper, self-adaptive real coded genetic algorithm (SARGA) is used as one of the techniques to solve optimal reactive power dispatch (ORPD) problem. The self-adaptation in real coded genetic algorithm (RGA) is introduced by applying the simulated binary crossover (SBX) operator. The binary tournament selection and polynomial mutation are also introduced in real coded genetic algorithm. The problem formulation involves continuous (generator voltages), discrete (transformer tap ratios) and binary (var sources) decision variables. The stochastic based SARGA approach can handle all types of decision variables and produce near optimal solutions. The IEEE 14- and 30-bus systems were used as test systems to demonstrate the applicability and efficiency of the proposed method. The performance of the proposed method is compared with evolutionary programming (EP) and previous approaches reported in the literature. The results show that SARGA solves the ORPD problem efficiently.     

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     

Clonal selection algorithm for power generators maintenance scheduling

This paper introduces a technique based on the one of the artificial immune system (AIS) technique known as the clonal selection algorithm (CSA) to obtain the optimal maintenance schedule outage of generating units. Based on a weekly load profile, the proposed technique provides the optimal maintenance window and calculates the optimal output power from each generator over a one year horizon. The maintenance scheduling problem is decoupled into two interrelated sub-problems namely, the maintenance scheduling and the power system sub-problems. The CSA is used to solve the maintenance scheduling subproblem to obtain the optimal maintenance outage of each unit. Based on the schedule generated by the CSA, the economic dispatch iterative lambda technique is used to find the optimal output power from each unit. Due to the search nature of the CSA, infeasible solutions may be introduced during the solution process. Therefore, a local search technique is used to watch the feasibility of the new solutions. The paper reports test results of the proposed algorithm to find the optimal maintenance schedule of the IEEE 30 bus system with 6 generating units and the IEEE 118 bus system with 33 generating units. Results are compared against the results obtained by complementary decision variables structure (CDV) and the evolutionary programming based techniques. Results are encouraging and indicate the viability of the proposed CSA technique.     

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.     

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.     

Binary fireworks algorithm for profit based unit commitment (PBUC) problem

The deregulation of electricity markets has transformed the unit commitment and economic dispatch problem in power systems from cost minimization approach to profit maximization approach in which generation company (GENCO)/independent power producer (IPP) would schedule the available generators to maximize the profit for the forecasted prices in day ahead market (DAM). The PBUC is a highly complex optimization problem with equal, in equal and bound constraints which allocates scheduling of thermal generators in energy and reserve markets with no obligation to load and reserve satisfaction. The quality of the solution is important in deciding the commitment status and there by affecting profit incurred by GENCO/IPPs. This paper proposes a binary coded fireworks algorithm through mimicking spectacular display of glorious fireworks explosion in sky. In deregulated market GENCO/IPP has the freedom to schedule its generators in one or more market(s) based on the profit. The proposed algorithm is tested on thermal unit system for different participation scenarios namely with and without reserve market participation. Results demonstrate the superiority of the proposed algorithm in solving PBUC compared to some existing benchmark algorithms in terms of profit and number of iterations.     

Integrating genetic algorithms, tabu search, and simulatedannealing for the unit commitment problem

This paper presents a new algorithm based on integrating genetic algorithms, tabu search and simulated annealing methods to solve the unit commitment problem. The core of the proposed algorithm is based on genetic algorithms. Tabu search is used to generate new population members in the reproduction phase of the genetic algorithm. A simulated annealing method is used to accelerate the convergence of the genetic algorithm by applying the simulated annealing test for all the population members. A new implementation of the genetic algorithm is introduced. The genetic algorithm solution is coded as a mix between binary and decimal representation. The fitness function is constructed from the total operating cost of the generating units without penalty terms. In the tabu search part of the proposed algorithm, a simple short-term memory procedure is used to counter the danger of entrapment at a local optimum, and the premature convergence of the genetic algorithm. A simple cooling schedule has been implemented to apply the simulated annealing test in the algorithm. Numerical results showed the superiority of the solutions obtained compared to genetic algorithms, tabu search and simulated annealing methods, and to two exact algorithms     

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.     

改进整数变量辨识方法在机组组合问题中的应用

如何辨识待定整数变量,是机组组合问题中的难点,为此在综合考虑机组不同出力水平对成本的影响、系统时段耦合、系统备用以及网络安全等约束的情况下,提出了待定整数变量辨识方法.首先对各线性化目标函数进行安全约束机组组合松弛计算,根据所得结果按给定规则确定所有在全时段机组状态出现启停的机组集合,有效缩小了机组组合的寻优空间.在不影响最优解的前提下,利用负荷曲线特异性截取技术,加速了待定整数集合识别过程,提高了计算效率.算例结果验证了该方法的有效性     

求解机组组合问题的改进离散粒子群算法

电力系统机组组合问题是一个高维数、离散、非线性的大规模复杂工程优化问题.文中提出了一种基于改进离散粒子群优化算法求解机组组合问题的新方法.首先采用新的策略生成粒子,以保证所有生成的粒子均为满足基本约束条件的可行解,使整个算法只在可行解区域进行优化搜索;然后引入优化窗口的概念和启发式的规则以缩短计算时间和提高优化精度.仿真结果表明所提出的算法具有解的质量高、收敛速度快的特点,充分证明了它能很好地解决机组组合问题.     

Fuel restricted short term economic dispatch using evolutionary programming for utility system

The objective of the paper is to minimize the production cost of the thermal power generation. An elegant approach is presented in order to obtain the equivalent cost function of the participating non-fuel restricted units and the Economic Dispatch Calculations (EDC) are carried out along with fuel restricted units. The Evolutionary Programming (EP) technique is used for real power optimization with fuel restricted units. The optimal solution is obtained neglecting losses. The Fast Decoupled Load Flow (FDLF) analysis is conducted to find the losses by substituting the generation values. Then the loss is participated among all generating units using participation factor method. The load flow is conducted again and the voltage limit violation is checked. The Algorithm is tested on IEEE 6-bus system IEEE 30-bus system and a 66-bus utility system. The results obtained by this new approach are compared with those obtained using classical method. It is observed that the proposed method is more reliable and efficient.     

基于SCUC的可入网混合电动汽车优化调度方法

在可入网混合电动汽车(PHEV)有望规模化应用的背景下,以传统的计及安全约束的机组最优组合(SCUC)问题为基础,发展了能够容纳PHEV的电力系统优化调度数学模型。所发展的模型以保证系统安全运行为前提,兼顾了PHEV车主的经济效益与发电的碳排放成本。利用PHEV作为可移动电量储存单元的特性,将模型解耦为机组最优组合与计及交流潮流约束的充/放电计划优化2个子模型。应用混合整数规划方法和牛顿—拉夫逊潮流算法迭代求解优化问题,可以同时获取日前机组调度计划和各时段的PHEV最优接纳容量及充/放电计划等结果。最后,以6节点和IEEE 118节点2个系统为例,验证了所构建模型的正确性和有效性。     

Improved artificial bee colony algorithm considering harvest season for computing economic dispatch on power system

This paper proposes the harvest season artificial bee colony (HSABC) algorithm, a novel improvement of the artificial bee colony (ABC) algorithm, for computing an economic dispatch solution of a power system based on fuel consumption and the produced emissions. A standard model of the power system, the IEEE‐62 bus system, is used to show the performance of HSABC using equality and inequality constraints to determine the optimal solution for the economic operation of the power system. Simulations involving the proposed algorithm show that HSABC has better ability to determine the minimum values for the operating cost problem with faster convergence and shorter running time when compared to the traditional ABC algorithm. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Unit commitment by an enhanced simulated annealing algorithm

A new simulated annealing (SA) algorithm combined with a dynamic economic dispatch method has been developed for solving the short-term unit commitment (UC) problem. SA is used for the scheduling of the generating units, while a dynamic economic dispatch method is applied incorporating the ramp rate constraints in the solution of the UC problem. New rules concerning the tuning of the control parameters of the SA algorithm are proposed. Three alternative mechanisms for generating feasible trial solutions in the neighborhood of the current one, contributing to the reduction of the required CPU time, are also presented. The ramp rates are taken into account by performing either a backward or a forward sequence of conventional economic dispatches with modified limits on the generating units. The proposed algorithm is considerably fast and provides feasible near-optimal solutions. Numerical simulations have proved the effectiveness of the proposed algorithm in solving large UC problems within a reasonable execution time.