Energy and Power Engineering, 2010, 2, 182-189
doi:10.4236/epe.2010.23027 Published Online August 2010 (
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
Received April 21, 2010; revised June 2, 2010; accepted July 10, 2010
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-
Copyright © 2010 SciRes. EPE
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
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
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
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,
Copyright © 2010 SciRes. EPE
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:
tt tt
is the effectiveness of the annual hydropower
is the comprehensive output co-
efficient of hydropower. t
P is the power price factor;
Q is the generating flow of hydroelectric power on the
time t (m3/s). t
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
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
maxmax min{}
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.
() ()
min ()
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:
min ()
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.
 (5)
where, 1t
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
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.
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.
where, ,mint
Q is the minimum discharge on the time t
(m3/s); ,maxt
Q is the maximum discharge on the time t
4) Hydropower station output constraint.
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-
Copyright © 2010 SciRes. EPE
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
ZZ Z), (222
), …, (123
nnn n
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:
min( ){( ),( ),,( )}
..()0, ,,
() 0,, ,
st gik
 
 
yx xxx
where, x is the decision vector. 12
(, , ,)
xx x
is decision space. y is the objective
function vector. 12
(, , ,)m
yy RyY. Y is obj-
ective space. ()fx is the objective function to be opti-
mized, ()
gx, ()
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()
x, and take the p-1 ob-
jectives as secondary targets, choose some threshold
values (2,3,,)
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.
min( )
..( ),
tx Sx Sfxu jp
  
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
Copyright © 2010 SciRes. EPE
(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:
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
max( ,)
tzet tt
Wh Wh (14)
where, ,
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-
ni ii
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
Step 4. Initialization. Choosing n different initial val-
ues and acquiring n chaotic variable serial ,ip
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)
is controlled parameter, if 0
, 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
 , 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.
Copyright © 2010 SciRes. EPE
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
 
) 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
composed of the ground n-vector, by Equation (18)
Find the Chaos decision vector '
after disturbance
(1 )
 
 (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( )
 (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
Copyright © 2010 SciRes. EPE
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
Increase the
proportion of annual
electricity output /%
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
Without ecology
benefit decrease
ratio /%
8.53 8.62 0.09 1.06
Copyright © 2010 SciRes. EPE
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. References
[1] J. D. C. Little, “The Use of Storage Water in a Hydroe-
lectric System,” Operational Research, Vol. 3, No. 2,
March 1955, pp. 187-197.
[2] Y. C. Zhang, F. S. Li, Y. F. Du, Y. F. Huang and S. Y.
Xiong, “The Optimization of Hydropower Station Res-
ervoir Dispatching,” in Chinese, Journal of Huazhong
University of Science and Technology, Vol. 9, No. 6, De-
cember 1981, pp. 49-56.
[3] W. Y. Tan, S. X. Huang, J. M. Liu and S. X. Fang, “Ap-
plication of Dynamic Programming in Optimizing the
Regulation of Reservoirs of Hydroelectric Stations,” in
Chinese, Journal of Hydraulic Engineering, Vol. 13, No.
135, July 1982, pp. 1-7.
[4] Q. Huang and Z. Q. Yan, “A Discussion on Methods of
Long-Term Optimal Operation of Hydropower Stations
Reservoir,” in Chinese, Journal of Hydro Electric Power,
Vol. 3, No. 3, March 1987, pp. 1-7.
[5] G. W. Ma, “Study on Stochastic Optimum Problems for
Multireservoir Hydroelectric Systems,” in Chinese, Jour-
nal of Xi’an University of Technology, Vol. 7, No. 4, De-
cember 1988, pp. 65-74.
[6] D. G. Shao, X. Y. Song, J. Xia and Z. Q. Sun, “Research
on Real-Time Optimal Flood Dispatching Model for
Yanghe Reservoir,” in Chinese, Advances in Water Sci-
ence, Vol. 10, No. 2, February 1999, pp. 135-139.
[7] J. Wan and H. Y. Chen, “A Study on Optimal Operation
of Hydropower Group by Combined Model of Decompo-
sition Coordination and Aggregation-Decomposition of
Large System,” in Chinese, Journal of Hydroelectric En-
gineering, Vol. 15, No. 2, February 1996, pp. 41-50.
[8] S. Y. Chen and H. C. Zhou, “Fuzzy Optimal Decision
Theory and Model of the Multistage and Multiobjective
System,” in Chinese, Water Resources and Power, Vol. 9,
No. 1, January 1991, pp. 9-17.
[9] W. Robin and S. Mohd, “Evaluation of Genetic Algo-
rithms for Optimal Reservior Resources,” Journal of Wa-
ter Resource Planning and Management, Vol. 125, No. 1,
January 1999, pp. 25-33.
[10] G. W. Ma and L. Wang, “Application of a Genetic Algo-
rithm to Optimal Operation of Hydropower Station,” in
Chinese, Advances in Water Science, Vol. 8, No. 3, March
1997, pp. 275-280.
[11] T. S. Hu, Y. H. Wan and S. Y. Feng, “Research on the
Artificial Neural Network Methodology for Multi-Res-
ervoir Operating Rules,” in Chinese, Advances in Water
Science, Vol. 6, No. 1, January 1991, pp. 9-17.
[12] S. H. Zhang, Q. Huang, H. S. Wu and J. X. Yang, “A
Modified Particle Swarm Optimizer for Optimal Opera-
tion of Hydropower Station,” in Chinese, Journal of Hy-
droelectric Engineering, Vol. 26, No. 1, January 1996, pp.
[13] G. Xu and G. W. Ma, “Optimal Operation of Cascade
Hydropower Stations Based on Ant Colony Algorithm,”
in Chinese, Journal of Hydroelectric Engineering, Vol.
24, No. 5, May 1991, pp. 9-17.
[14] L. S. Suo, “Water Conservancy’s ‘Special Features’—
The New Ideas about the Water Conservancy Construc-
tion,” in Chinese, China Water Resources, Vol. 38, No. 1,
January 2003, pp. 25-26.
[15] Z. R. Dong, D. Y. Sun and J. Y. Zhao, “Multi-Objective
Ecological Operation of Reservoirs,” in Chinese, Water
Resources and Hydropower Engineering, Vol. 38, No. 1,
2007, pp. 28-32.
[16] G. W. Ma, L. Wang and X. M. Guo, “A Optimal Opera-
tion Model for Multiple Reservoir Power with Time-
Varying Electricity Price,” in Chinese, Advances in Water
Science, Vol. 13, No. 5, May 2002, pp. 583-587.
[17] H. P. Hu, D. F. Liu and F. Q. Tian, “A Method of Eco-
logical Reservoir Reoperation Based-on Ecological Flow
Regime,” in Chinese, Advances in Water Science, Vol. 19,
No. 3, 2008, pp. 325-332.
[18] W. G. Yu, Z. Q. Xia and G. R. Yu, “Analysis of Eco-
logical Ideas and Measures in Reservoir Scheduling,” in
Chinese, Journal of Shangqiu Teachers College, Vol. 22,
No. 5, 2006, pp. 148-151.
[19] E. N. Lorenz, “Deterministic Non-Periodic Flow,” Jour-
nal of Atomsphere Science, Vol. 20, No. 2, June 1963, pp.
[20] B. Li and W. S. Jiang, “Chaos Optimization Method and
its Application,” in Chinese, Control Theory and Appli-
cations, Vol. 14, No. 4, April 1997, pp. 613-615.
[21] L. Qiu, J. H. Tian, C. Q. Duan, X. N. Chen and Q. Huang,
“The Application of Chaos Optimization Algorithm in Res-
ervoir Optimal Operation,” in Chinese, China Rural Water
and Hydropower, Vol. 30, No. 7, July 2005, pp. 17-19.
[22] W. Liang, S. L. Chen, C. Y. He, D. Y. Liu and J. Rui, “Op-
timal Operation of Cascaded Hydropower Stations Based on
Chaos Optimal Algorithm,” in Chinese, Water Resources
and Power, Vol. 26, No. 1, January 2008, pp. 63-66.