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Energy and Power Engineering, 2010, 2, 182-189 doi:10.4236/epe.2010.23027 Published Online August 2010 (http://www.SciRP.org/journal/epe) Copyright © 2010 SciRes. EPE Chaotic Optimal Operation of Hydropower Station with Ecology Consideration Xianfeng Huang1, Guohua Fang1, Yuqin Gao1, Qianjin Dong2 1College of Water Conservancy and Hydropower, Hohai University, Nanjing, China 2College of Water Resources and Hydropower, Wuhan University, Wuhan, China E-mail: hxfhuang2005@163.com Received April 21, 2010; revised June 2, 2010; accepted July 10, 2010 Abstract Traditional optimal operation of hydropower station usually has two problems. One is that the optimal algo- rithm hasn’t high efficiency, and the other is that the optimal operation model pays little attention to ecology. And with the development of electric power market, the generated benefit is concerned instead of generated energy. Based on the analysis of time-varying electricity price policy, an optimal operation model of hydro- power station reservoir with ecology consideration is established. The model takes the maximum annual power generation benefit, the maximum output of the minimal output stage in the year and the minimum shortage of eco-environment demand as the objectives, and reservoir water quantity balance, reservoir storage capacity, reservoir discharge flow and hydropower station output and nonnegative variable as the constraints. To solve the optimal model, a chaotic optimization genetic algorithm which combines the ergodicity of chaos and the inversion property of genetic algorithm is exploited. An example is given, which shows that the pro- posed model and algorithm are scientific and feasible to deal with the optimal operation of hydropower station. Keywords: Hydropower Station Operation, Ecology, Chaotic Genetic Optimization Algorithm, Time-Varying Electricity Price 1. Introduction The optimal operation of hydropower station can increa- se the hydropower market competitive ability and realize the optimization of resources. How to manage and utilize the present hydropower station and to obtain the more comprehensive benefits in the case of maintain the extra investment, which have important significance on the development of our national economy and society and solve the problem of the energy shortage in short time. Investigation into the hydropower station optimal opera- tion arises from the 1940s, in 1946, Masse the first in- troduced the concept of optimization into hydropower station optimal operation. American scholar Little [1] propose a random model of reservoir optimal operation which random variable is the runoff. Now, many schol- ars carried out earlier reservoir optimal operation of rese- arch and application [2-5]. At present hydropower station reservoir operation have more research on optimization algorithm and reached many great results. Many arith- metic have been applied to hydropower station reservoir optimal operation [6-13], such as dynamic programming, decomposition-coodination method of large systems, fu- zzy mathematics, genetic algorithm, artificial neural net- work, particle swarm optimization algorithm, ant colony optimization algorithm. With the continuous develop- ment of theory and method for reservoir optimal opera- tion and in-depth development of electricity market re- form, the study of hydropower station reservoir optimal operation is a hotspot research within a period of time in the future. In addition, with the development of people’s knowledge about the ecological environment, some scho- lars become to concern the ecology for optimal operation of hydropower station [14,15]. But most studies of the existing reservoir are also rarely considered the ecologi- cal water requirements of the river downstream and the reservoir itself. Although the models and algorithms have made considerable progress, but most of the models and the algorithms have bad universality, and is often for the specific reservoir conditions and operating character- istics which develop the specific model and algorithm. In this paper, based on the predecessors, under the condi- tions of researching the electricity market, reasonable consider the ecological water requirements, the chaotic optimal operation model based on time-varying electric- X. F. HUANG ET AL. Copyright © 2010 SciRes. EPE 183 ity price is established, chaotic genetic arithmetic(CGA) is exploited to solve the model, the study has a certain reference practice value for optimal operation of hydro- power station. 2. Time-Varying Electricity Price In electric power market, competition system is intro- duced, and the policy of time-varying electricity price, such as flood and dry power price, peak and valley pow- er price is carried out. The key of hydropower compa- nies’ business is to achieve the maximum power genera- tion benefit considering the various constraints, through optimal arranging the generation process. Due to the characteristic of hydropower, such as the uncertainty and randomicity of runoff, the regulating ability of reservoir, the hydropower station reservoir optimal operation is much more complex. So, how to forecast the reservoir runoff, how to reasonably arrange generation operation to improve the economy benefit based on integrated uti- lization request and the regulating ability of reservoir and the flood and dry power price, become more and more important. In electric power market, hydropower companies par- ticipate in market competition through declaring energy price curve. Because the policy of “plant and network se- paration, electricity price bidding” is carried out, the tra- ditional optimal operation is challenged. The surround- ings up against the hydropower plant have changed pro- foundly, and so the optimal objective of hydropower plant. Along with the independency of property right of hydropower companies, the maximum income and profit is pursued. The rule of maximum power generation en- ergy in the past is substituted by the power generation benefit in the electric power market. In the condition of electricity price bidding, the opti- mal operation of hydropower station reservoir considers not only the water quantity factor, but also the electricity price factor. At the view of market economy, the hydro- power plants pay more attention to the timeliness of power generation energy and acquire more economic benefit. In the past few years, especially in the summer, power consumption load has increased rapidly. Many provinces of China suffer the lack of electricity. Besides, people’s life habit in a day makes the electricity load high in the day, and low in the night. The big difference of peak and valley usually causes some bad effects for power system, such as causing the operation difficulty, depressing the economy of the system. The best method to solve the problem is carrying out flood and dry power price and peak and valley power price. That is to say, the power price falls in the flood season, and increases in the dry season. It forms a net power price structure with price difference in different seasons. The peak and valley pow- er price includes peak load power price, valley load power price and smooth load power price which ascer- tained by the peak load period, valley load period and smooth load period in the daily load curve [16]. The time-varying electricity price can promote uses to avoid peak, and make the best of valley load. It can make the distribution of the power load curve uniform. In addi- tion, at the view of consumer demand and provider bene- fit, the policy of time-varying electricity price can in- crease power energy sales, reduce generation cost and improve the system operation benefit. In the other hand, it can provide preferential electricity price, save the expen- se for uses. So it is favorable for consumer and provider. The one-part rate system price is fixed and unchangeable, and the income of hydropower companies is the product of generated energy and power price. That is to say, the maximum benefit is equal to the maximum of generated energy. But for the time-varying electricity price, the two are different. So the optimal operation based on time-vary- ing electricity price is a new research problem for hy- dropower station reservoir. 3. Optimal Operation Model with Ecology Consideration 3.1. Guidelines for Optimal Scheduling Optimal scheduling of hydropower station reservoir op- timization operation is generally divided into two groups: the quantity and quality, including which makes the greatest economic benefits of electricity generation and makes the highest quality of electricity and water supply. From the economic point of view the biggest, in the ab- sence of the implementation of power market, for hydro- power station, the most common method is to make a maximum generating capacity in operation period. Under the environment of electricity market, the most important is to combine the electricity price, in accordance with peak and valley changes in policy, make reasonable ar- rangements for generation companies which owned the water and thermal power generation capacity at different times, and then the power companies can get the most economic benefits in operation period. 3.2. Objective Functions In order to achieve the most optimal use of water re- sources, in this study, the goal is to meet the premise of water requirements, the criterion is to improve the power generation companies’ earnings, and provide the greatest possible reliability and power to the grid, so, choose the following two objectives: Objective I: Obtain the maximum annual power gen- eration benefit per every year, by the reservoir regulation, X. F. HUANG ET AL. Copyright © 2010 SciRes. EPE 184 so as to increase the profit of hydropower station in the dry season and flat-water period, and then increase rev- enue generation as much as possible in the wet period. The objective can be seen as follows: 1 max T tt tt t F Ap Q HM (1) where, F is the effectiveness of the annual hydropower generation(RMB). A is the comprehensive output co- efficient of hydropower. t P is the power price factor; t Q is the generating flow of hydroelectric power on the time t (m3/s). t H is the average water head of hydroe- lectric power on the time t(m). T is the hydropower operation calculation of the total time. t M is the num- ber of hours in the time t. Objective II: Obtain the maximum output of the mini- mal output stage in the year. The objective can be seen as follows: maxmax min{} tt NPAQ H (2) where, NP is the maximization minimum output of hy- dropower station (MW). Other symbols are the same as (1). Objective III: Obtain the minimum amount of ecology- ical water shortage for river downstream and the reser- voir itself. () () t1 min () N tt Z RL VL (3) where, Z is the total ecological water shortage. ()t RL is the ecological water shortage of the river downstream at time t. ()t VL is the ecological water shortage of the res- ervoir itself at time t. N is the total time. Ecological water demand computing [17,18]. As the ecological water requirements of surviving in the de- bate, some scholars have raised the minimum ecologi- cal water and suitable ecological water demand, water demand of ecological environment in this article is based on the minimum water volume of ecological wa- ter demand on the basis of calculation. Therefore, (3) can be written as: ()()()() t1 min () N tttt Z RD VDRSVS (4) where, ()t RD and ()t VD are the minimum amount of ecological water demand of the river downstream and re- servoir itself respectively. ()t RS and ()t VS are the sup- ply amount of ecological water of the river downstream and reservoir itself respectively. The traditional optimal operation of hydropower reser- voir main considers socio-economic objective, with little regard the requirements of the ecological environment, leading to environmental degradation. The objective of minimum ecological water shortage of river downstream and reservoir fully reflects the lower reaches of the res- ervoir and river ecology to environmental protection, so that human life and the ecological environment has been the basic water was placed in the same the degree of im- portance for the protection of river health, and promote sustainable utilization of water resources play an impor- tant role. 3.3. Constraints 1) Reservoir water balance constraint. 1() ttttt VVqQK (5) where, 1t V is the reservoir storage capacity in the end of time t(m3); t V is the reservoir storage capacity in the beginning of time t(m3); t q is the average inbound flux on the time t (m3/s); t K is the conversion factor of the time length. 2) Reservoir storage capacity constraint. At any time, the reservoir water storage capacity storage capacity should be kept between a minimum and maximum vol- ume of water. ,min,maxttt VVV (6) where, ,mint V is the allowed minimum reservoir capacity on the time t (m3). ,maxt V is the allowed maximum res- ervoirs capacity on the time t (m3). 3) Reservoir discharged flow constraint. ,min,maxttt QQQ (7) where, ,mint Q is the minimum discharge on the time t (m3/s); ,maxt Q is the maximum discharge on the time t (m3/s). 4) Hydropower station output constraint. ,min,maxtttt NAQHN (8) where, ,mint N is the minimum output which hydro- power station allowed, it is always the guaranteed output (kW). ,maxt N is the maximum output which hydropower station allowed, it is always the installed capacity (kW). 5) Nonnegative variable constraint. All of the above decision variables are non-negative variables(≥ 0). 4. Chaotic Genetic Algorithm 4.1. Thought of Chaotic Genetic Algorithm Chaos is a seemingly rule, similar to the random phenol- menon which emerge in deterministic system, the theo- X. F. HUANG ET AL. Copyright © 2010 SciRes. EPE 185 ries marked by the United States meteorologist Lorenz in 1963, which published papers named “Deterministic non-periodic flow” [19], this paper reveals the existence of deterministic chaos in nonlinear equation. Nowadays, scholars generally agreed that chaos with such features, include randomness, regularity, and ergodicity [20], due to chaotic motion can after all states according to their own laws within a certain range of non-repetition. There- fore, use chaotic variables to optimization search, certainly the global optimal solution can be obtained and have high search efficiency. At present, the chaos optimization have been applied in optimal operation of reservoirs [21, 22], on the basis of previous research, this paper coupled the chaos optimization and genetic algorithms, combined with multi-objective decision-making techniques to deve- lop the chaotic genetic algorithm (CGA). The first, CGA use constraint method converted multi-objective problem to single objective problem, using penalty function me- thod dealing with constraints. And then chaotic variables were introduced into the optimization variables, and to enlarge the scope of chaotic motion to the range of opti- mization variables, code chaotic variables which we got, using the search mechanisms of genetic algorithm to obtain the optimal solution. The basic idea of CGA solv- ing hydropower station reservoir optimal scheduling is: the first, scheduling period (usually one year) is divided into a number of time slots T, numbered the sequence numbers of each period, choose every period of the res- ervoir water level value (the value of reservoir storage capacity can also be used) as optimization variables, de- termine the upper and lower limits of the reservoir water level value each time, randomly selected n different ini- tial values which interval is between 0 and 1, through Logistic maps can obtain the n-chaotic trajectories of different sequence, the length of the chaotic sequence is the population size, large it to the range of reservoir wa- ter level at all times, then get n group sequence of the reservoir water level which stand forthe reservoir op- eration control process (111 1 123 ,,,, T Z ZZ Z), (222 123 ,,, Z ZZ 2 ,T Z ), …, (123 ,,,, nnn n T Z ZZ Z), and as a mother, accor- ding to the intended target function evaluate its advan- tages and disadvantages, calculate the fitness value of all chromosomes, carry out selection, crossover and muta- tion operations according to the chromosomes fitness, use the most excellent retention strategy, abandon the low fitness chromosomes, to retain the high fitness chr- omosomes, and thus get new groups. Add a chaotic small perturbation to the optimization variables, by evolving from generation to generation, then finally converge to one individual which in the most suitable environment, and obtain optimal solution to the problem. 4.2. Multi-Objective Decision The basic springboard of chaotic optimization is the er- godicity, that chaotic motion can pass all states nonre- curring in a certain range. The characteristic can be ef- fective mechanism of avoiding local optimal solution and the difficulty of the continuity and differentiability of objective functions and constraints. The idea of chaotic optimization is to transfer area coverage from chaotic series to decision variables, use the new chaotic variables for searching and iterative comparison. If the criterion of stop is satisfied, then export the optimal results. Mathe- matically, the general multi-objective constrained opti- mization problem can be stated as follows: 12 min( ){( ),( ),,( )} ..()0, ,, () 0,, , m i j ffff st gik hjl yx xxx x x (9) where, x is the decision vector. 12 (, , ,) n x xx x n R X . X is decision space. y is the objective function vector. 12 (, , ,)m m y yy RyY. Y is obj- ective space. ()fx is the objective function to be opti- mized, () i gx, () j hx are the constraints imposed on the design, n, m (m > 1) are the dimensions of decision vector and objective functions respectively. For multi-objective optimization problem, it is diffi- cult to find absolute optimal solution. Mostly, we choose the best equilibrium solution which has precision to a certain extent and practical significance according to the request of problem. Traditional multi-objective programming method is linear weighted sum method. It converts the problem to single objective problem by weighted coefficient. There are some disadvantages such as the units of different objectives are not the same for comparison and subjec- tivity is obvious. This paper adopts constraint method. Supposing the problem has p objectives. The idea is to ascertain a main objective 1() f x, and take the p-1 ob- jectives as secondary targets, choose some threshold values (2,3,,) j uj p through the experience of deci- sion-makers, then change the secondary targets to con- straints. So the problem is to solve the single objective optimal problem as follows. 1 min( ) ..( ), jj fx s tx Sx Sfxu jp (10) 4.3. Constraints Treatment Chaotic optimization is a direct search method, which re- quests dealing with the constraints. Penalty function method is effective for the constraints treatment. Its basic idea is to add a penalty item to the objective function as X. F. HUANG ET AL. Copyright © 2010 SciRes. EPE 186 (11), converting the initial problem to the new non-res- traint optimization problem with the penal function, was- hing out the non-feasibility solution through punishing the solutions dissatisfying the constraints and finally gaining the optimal solution. (, )()(())pfc xxx (11) where, ()fx is the objective function of initial problem, (( ))c x is the penalty item. The paper adopts non-differentiable exact penalty func- tion method to convert the constraints to non-restraint optimization problem. It avoids the sequence character in computation, accords the solution of restraint optimiza- tion with the minimum points of penalty function. It also avoids the difficulty of the non-differentiability, which is effective for the optimization without grads information. With the work upwards, multi-objective restraint optimi- zation problem is converted to single objective non-re- straint optimization problem. In the paper, objective II and objective III is trans- ferred into constraints by non-differentiable exact pen- alty function method. The specific action is: firstly, am- plification to guaranteed output, as lower limit output of the minimum time output. The value needs several trials. Secondly, the minimum ecological water shortage objec- tive will be transferred to two constraints, one is to meet the minimum ecological water demand of river down- stream, and the other is to meet the minimum ecological water demand of the reservoir itself. The objective II can be transferred to guaranteed out- put constraints as follows: 0tt A QH N (12) where, 0 N is the amplified guaranteed output. The objective III can be transferred to ecological water demand constraints. Considering the ecological hydropo- wer station reservoir operation, the reservoir and down- stream of the ecological and environmental problems were emphatically solved, the following river ecological water requirements lower bound to determine the process of ecological environment of the reservoir discharged. Therefore, the ecological water demand constraints in- cluding two aspects: ecological storage capacity constra- ints and the downstream of ecological water demand constraints. , max( ,) tzet tt VL VVVH (13) mintt Wh Wh (14) where, , z et V is the ecological environment storage ca- pacity of reservoir; t VL is the dead storage capacity of reservoir; t VH is the beneficial capacity in non-flood period, in flood period is the flood control storage capac- ity; t Wh is the discharged ecological flow of reservoir in time t period; minl Wh is the minimum ecological wa- ter demand of downstream in time t period. 4.4. Steps of CGA The idea of multi-objective chaotic genetic optimization algorithm is to decompose the problem into a single un- constrained optimization problem. Chaotic optimization theory and genetic algorithm are coupled to solve the optimization problem. The steps of CGA are as follows: Step 1. Multi-objective decision. Constraints method is used to deal with the multi-objective problem. The problem is transformed into single problem by (11). Step 2. Constraints treatment. Non-differentiable exact penalty function method is used to deal with the cons- traints. We choose a certain penal factor to constitute pen- alty item. The problem is converted into the non-restraint optimization problem according to (15). Then we gain the optimization problem of continuous object as fol- lows: 12 min(,,,)[, ni ii f xxxxab in (15) Step 3. Parameters setting. Ascertaining the numbers of variables is n, and the bounds is [ai, bi], the population scale of genetic arithmetic is M, the maximal iteration times of the arithmetic is T, the cross probability of crossover probability is Pc, the mutation probability is Pm. Step 4. Initialization. Choosing n different initial val- ues and acquiring n chaotic variable serial ,ip through Logistic mapping. 1, 2,,in , p is the length of the chaotic variable serial. Logistic mapping is as follows: ,1 ,, (1 ) ijij ij , 0,1, 2,,1jp (16) where, is controlled parameter, if 0 01 , 4 , then the (11) is in chaotic status and has all char- acteristic of chaotic motion. Step 5. Magnify the ranges of chaotic series into the confines of optimal variables with (17). ,, () ijiii ij xaba , 1, 2,,jp (17) Step 6. Fitness function values calculation. Choose a proper fitness function to calculate the fitness value. Fit- ness value will be sorted in descending, select the 10 percent group on better fitness directly into the next gen- eration of groups, all populations of the selection, cross- over and mutation were carried out. Step 7. Calculate the new fitness value and make ad- justments, and sort the group according to the fitness value, then replace the worst of which 10% of fitness, and maintain the files. Calculate the average fitness value and compare with the maximum, if within the allowable error, then end the searching process, output the optimal solution, otherwise continue. X. F. HUANG ET AL. Copyright © 2010 SciRes. EPE 187 Step 8. Plus a chaotic disturbance to the current gen- eration of group fitness value less than 90 percent of the corresponding optimization variables, through the carrier means mapped to optimization variables, perform itera- tive calculation, with the increase of iterations number, iteration gradually approach to the optimal solution. Un- til the time, two figures out the difference between the average fitness is less than a pre-given small positive number. Chaotic disturbance can be done as follows: the number of iterations to meet the initial optimal solution (12 ,,, n x xx ) is mapped to (0,1) interval, the optimal decision by the initial vector, denoted by ' , the chaotic mapping function iteration times K get chaotic sequence (K is the length of the chaotic sequence), set k in the chaotic sequence of the k value (1, 2,,kK), write k composed of the ground n-vector, by Equation (18) Find the Chaos decision vector ' k after disturbance '' (1 ) kk (1, 2,,kK) (18) The formula for the (0,1), a value range can be adaptive selection, search the initial large, late small, according to (19) to determine : 1 1( ) m k k (19) The formula m for a positive integer, determined acco- rding to the number of objective function, generally gr- eater than or equal to 2; k for the chaotic map iterations. Step 9. According to the fitness value, resort the groups, calculate the average fitness and compare it with the maximum. If it is in the allowable error, end the process of optimization, and output the optimal solution, otherwise, go to Step 5. 5. Case Study Study a certain hydropower station data as an example. The curve between reservoir capacity and water level up- stream and the curve between water levels downstream with discharge of the hydropower station reservoir are given. The total reservoir capacity is 896 million m3, regulating capacity is 445 million m3, the normal water level is 977.0 m, dead water level is 948 m, flood-control water level is 966.0 m. The coefficient of output power takes 8.3, guaranteed output is 185 MW. Installed capac- ity is 1080 MW. The largest discharge is 1000 m3/s. Ac- cording to the time-sharing surfing electricity price pol- icy, in dry season period on the basis of the flat water floating upward 50 percent, in flood period, it falls 25 percent on the basis of the flat water. In flat-water period, the benchmark price is 0.247 RMB/kW·h, in dry season the floating price coefficient (December-next April) is 1.50, in flat-water period (May and November) is 1.00, and in flood period (June-October) 0.75. In a day, the power price of normal period is carried out by regulation, spike and peak hours floating upward 22 percent, and valley hours fall 40 percent. According to the annual average runoff data, the fore-mentioned model and CGA is used for optimal operation. The initial population of the model takes 2000. Crossover probability takes 0.9. Mutation probability takes 0.1. Permitted error takes 1.0 × 10-8. The largest iteration number takes 50. Logistic mapping initial value takes the values belong to [0.51, 074]. The software of MATLAB is used for calculation. The program runs 10 times, and we take the best result of them. In each program runs, the results of each genera- tion to be superior than the previous generation, or the results equal to the previous generation, it is the result of using the optimal retention policies. The final results can be seen in Table 1. The ecological water demand of the river downstream is calculated by Tennant method and minimum monthly runoff method, and takes the bigger. The ecological wa- ter demand of the reservoir itself is less than dead storage reservoirs 451 million m3, so the smallest ecological wa- ter demand of the reservoir itself is met. Table 1. The result of optimal operation of hydropower station in electricity market environment. Month Initial level /m Final level /m Generating flow /m3/sOutput /104 KwGenerated energy /108 Kw·h Generated benefit /108 RMB 7 976.47 966 945.48 53.03 3.87 1.43 8 966 948 1273.16 55.59 4.06 1.50 9 948 948 1254.29 45.44 3.32 1.23 10 948 976.56 766.30 37.62 2.75 1.02 11 976.56 976.97 535.05 33.03 2.41 0.60 12 976.97 976.79 330.70 20.65 1.51 0.28 1 976.79 976.65 343.55 21.39 1.56 0.29 2 976.65 976.91 382.60 23.80 1.74 0.32 3 976.91 976.58 601.90 37.04 2.70 0.50 4 976.58 979.96 493.82 31.17 2.28 0.42 5 979.96 976.53 322.40 20.50 1.50 0.37 6 976.53 976.47 337.15 20.94 1.53 0.57 Total 29.21 8.53 X. F. HUANG ET AL. Copyright © 2010 SciRes. EPE 188 From Table 1, the initial and the final water level are meeting the upper and lower limits. The output value of each month is also within the control range. Generating flows of each month are also meeting the ecological wa- ter demand of flow downstream. Therefore, the results meet the requirements. In order to illustrate the superiority of the algorithm, four kinds of methods including dynamic programming (DP), genetic algorithm (GA) and chaos optimization algo- rithm (COA) were used in this paper, use the four kinds of methods to calculate the hydroelectric reservoir opti- mal operation model, the results can be seen in Table 2. From Table 2, CGA has the best results, next are the GA and the COA, and finally is the DP. DP needs the state discrete-time and stores state information in the optimiza- tion. The more discrete points it has, the higher precision it gets. But it increases the optimization run-time very much. GA depends on random variables, and it does not need the storage of eliminated discrete points. Therefore, it shows an obvious superiority in solving these optimization prob- lems. So for the same problems, GA can greatly save the computer’s memory demand. However, because of the probability search features, the results of GA are unstable. COA maps the chaotic sequences which generate by Lo- gistic mapping to the range of optimal variables, and then does iterative searching, fully using the ergodicity charac- teristic of chaotic optimization. The annual generating capacity which is calculated by COA is greater than that of DP, but it needs larger chaotic sequence length, the time consuming of the program is longer. Therefore, the search efficiency of COA needs to be improved. CGA combines the advantages of GA and COA, using the ergodicity feature of chaotic optimization, mapping the chaotic sequences which generated by Logistic mapping to the ranges of optimization variables, and then using the optimization mechanism of genetic algorithm for selection. After crossover and mutation, a chaotic disturbance is added to the variables corresponding to the degree of op- timization variables in the current generation of groups, and then carrying out the genetic manipulation until the termination of the proceedings meets the conditions. Fi- nally, output the optimal solution. Therefore, CGA has the advantages of high efficiency, good convergence per- formance and it approaches to the global optimal solution better. So it is the best algorithm to solve the optimal op- eration of hydropower station reservoir. Of course, due to the need of larger population size to achieve ergodicity, the calculation time of CGA is longer than GA. The paper also does the research that not considering the ecology. The objectives take the largest generated benefit and the maximum output of the minimal output stage in the year. The generated energy of hydropower reservoir optimal operation is 8.62 billion RMB without ecology consid- eration, which is 9 million RMB more than that with ecology consideration. But in January and February, the generating flow is less than the minimum ecological wa- ter flows. The results can be seen in Table 3. Can be seen from Table 3, without considering the eco- logical optimal operation of hydropower generating capac- ity of the reservoir and consider the ecological results of optimal operation of hydropower station reservoir compared to an increase of only 0.09 million RMB about 1.06%, the two are close, But do not take into account the environment of the river hydropower reservoir optimal operation of the negative environmental impact is far-reaching. Optimal operation of hydropower and ecological considerations will help protect the river environment and promote sustainable use of water resources; sacrifice in exchange for a small part of the power generation efficiency and harmonious social and economic development and ecological environment is worth it and very necessary. 6. Conclusions In electric power market, as a result of “separate the sta- tion and network, price bidding”, and the independent property of all generating companies, the focus of opti- mal operation for the power plant transforms from single safety production to taking economic benefits as central of all-round integrated development. Power generation benefit will be paid more attention by generation compa- nies. In this paper, a multi-objective chaotic optimal op- eration model based on time-varying electricity price is established in electric power market, considering the eco- logical water requirements of downstream. To solve the model, a multi-objective chaotic genetic optimization algorithm is exploited, which has the advantages of high search efficiency, good convergence performance, faster pace converge to the global optimal solution. It greatly increases the efficiency and effectiveness of optimal op- eration, and enriches and develops the theory and method of optimal operation for hydropower station reservoir. Table 2. Results calculated by different algorithms. Algorithms Optimal results /108RMB Increase the proportion of annual electricity output /% Time consuming /s DP 8.24 1.10 10.4 GA 8.51 3.86 54.9 COA 8.39 2.74 387.3 CGA 8.53 6.23 265.2 Table 3. Results with and without ecology consideration. With ecology Consideration /108RMB Without ecology consideration /108RMB Generated benefit decrease /108RMB Decrease ratio /% 8.53 8.62 0.09 1.06 X. F. HUANG ET AL. Copyright © 2010 SciRes. EPE 189 As the development of people’s consciousness about the ecological environment and the idea of harmonious coexistence between human and nature, the ecology is necessary in optimal operation of hydropower stations. The paper takes full consideration of the ecology water demand of the river downstream and the reservoirs itself. In the actual calculations, the objective is solved through the constraint method. The example shows that the result without ecology consideration is a little more than that with ecology consideration, but the negative environ- mental impact is far-reaching. 7. Acknowledgements The authors wish to thank Yinqin CHEN of Nanjing Un- iversity of Technology for her careful review and cons- tructive modifications. And the work is supported by the The National Natural Science Fund of China (No. 50909073) and Natural Science Fund of Hohai Univer- sity (No.2009422011) and the Fundamental Research Funds for the Central Universities (2013B1020084). 8. 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