CC BY
8
УДК 621.565:536.58
Optimal design of a wind system for water pumping. Using a genetic algorithm
Ph. D. G. C. SEMASSOU1, Ph. D. C. DANGBEDJI, Ph. D. G. DEGAN2
Ph. D. A. VIANOU3 [email protected], [email protected], [email protected]
University of Abomey- Calavi, Benin Ph. D. T. C. GUIDI4 [email protected] University Institute of Technology Lokossa, Benin D. Sc. L. V. GALIMOVA5 [email protected] Astrakhan State Technical University, Russia Ph. D. J.-P. NADEAU6 [email protected] Institut de Mécanique et Engineer, France
This article presents the design of a wind pumping system coupled to a reservoir of water storage. This work has been done with the HOGA program (Hybrid Optimization by Genetic Algorithms). Different objective functions used in the design process are the loss of power probability (LPSP), concept for the reliability, the life cycle cost (LCC) for the economic evaluation and CO2 emissions of life cycle on the production of the various system components. With the presented model, the optimization of the design of wind pumping system can be realized technically, economically and environmentally, while ensuring the needs of the consumer without interruption. Design variables used are the wind turbines number NW the type of wind TW the tank number NKmk, the type of tank Tfank, type mast Ttowr and total head Tkad, that is to say the type of well. A case study is conducted to analyse one wind turbine pumping projet, which is designed to supply drinking water in a rural community located at Seme-Kpodji, Benin (6°22'N, 2°37'E, 7m).
Keywords: wind turbine; optimization; motor-pump model; desirability, objective function, genetic algorithm.
Оптимальное проектирование насоса с ветряным двигателем для откачки воды с использованием генетического алгоритма
Канд. техн. наук Г. К. СЕМАСУ, канд. техн. наук С. ДАНГБЕДЖИ, канд. техн. наук Ж. ДЕГАН, канд. техн. наук А. ВИАНУ, канд. техн. наук Т. К. ГУИДИ, д-р техн. наук Л. В. ГАЛИМОВА, канд. техн. наук Ж.-П. НАДО
Статья рассматривает вопросы проектирования насоса с ветряным двигателем, соединенного с резервуаром для хранения воды. В процессе проектирования используются такие целевые функции как вероятность потери мощности, принцип надежности, экономические издержки жизненного цикла и уровень выбросов С02различных компонентов системы. Представленная модель оптимизирует конструкцию насоса с ветряным двигателем с технической, экономической и экологической точки зрения, бесперебойно обеспечивая при этом потребности потребителя. Используются следующие переменные: количество ветровых турбин тип ветра Тп, число резервуаров Ntank, тип резервуара Т1апк, тип мачты Т1дпег и суммарная высота напора ТНеш1 — т. е. тип колодца. Исследование проводится на примере анализа работы насоса с ветряным двигателем, предназначенного для обеспечения питьевой водой сельской общины Семе-Кпожи, Бенин (6°22'М, 2°37'Е, 7м).
Ключевые слова: ветровая турбина; оптимизация; модель насоса с двигателем; желательность, целевая функция, генетический алгоритм.
Introduction
Water is a vital element and covers about 70% of the surface of the planet. It is used to supply drinking water for people, livestock, irrigation, etc. The alarming deterioration of the water quality and the growing inequality of water resources coupled with reduced rainfall in many arid countries pose serious problems in terms of health, urban planning, economics, brief
development. Today, many African countries are experiencing a great crisis of drought. Faced with this situation, a question arises: how to power these water populations, whose absence is a factor of the underdevelopment? Groundwaters seem to be the only alternative to this dilemma; but all is not enough to have groundwater; it is indispensable to develop technology for pumping the water extraction. Pumping water
has become in our days a major issue for the improvement of living conditions and socio-economic development of rural communities. Several technologies make it possible today to bring a valid, durable and clean solution. Pumping systems are distinguished according to their energy source: Manual — pedal — powered by animal traction — wind — a diesel generator respectively gasoline — photovoltaics. However, pumping systems for wind, photovoltaics are becoming more attractive and compete from cost perspective and performance with systems using conventional energy sources. Systems powered by renewable energy sources (solar and wind) are particularly useful in remote areas where fuel supply is problematic. Benin has in its southern part some wind corridors that are conducive to the development of wind mills of pumping. In the literature, several studies have been made in the field of water pumping for water supply of the population. Thus, some authors have developed physical models of various components of a hybrid energy system or not and others have developed a methodology for estimating the economic and energy cost over the life cycle of sub-components of these systems [10, 12, 17, 19]. With present design methods, the size of the tank is often coarsely estimated. Thus, in the case of too small a tank, there has been overflow of water. As against, over-sized with a reservoir, may be present in construction costs too high. In this paper the optimization of a Wind system, with water storage tank (see Fig. 1) to supply the electrical
demand for water pumping in a small town located near Cotonou (Benin) is described. The optimization is based on the concepts of minimization of LPSP (the power supply loss probability), the life cycle cost (LCC) for the economic and CO2 emissions. The NSGA-II algorithm, evolutionary genetic type was used in order to determine the set of optimal compromise solutions, which are ranked in descending order according to their desirability. The method used is declined in four steps. Firstly we proceed to the analysis of the water needs of the locality, then draw up models of the various components of the system, then defines the performance criteria and the different rates of satisfaction and finally proceeds to the classification and selection of solutions.
Materials and methods
1. Consumption profile adopted and Wind Data
Water requirements of the selected location are not negligible. The final water uses distribution obtained in this study is the following: faucets (39.20%), toilets (22.2%), showers (19.9%), clothes washers (9.7%) and finally leaks (8.9%) (See Fig. 1a).
Consumption is not constant every day of the year; it fluctuates according to the months of the year, according to the weeks of the month, the days of the week and different times of the day. This variation reflects in the time the rhythm
3,5
3 3 Й
О
U 2,5
e
s 2
с z с
0
"-1 1 5
"ё
1 1
J 0,5 К
0 2 4 6 8 10 12 14 16 18 20 22 24 Hour
a b
Fig. 1. Water use: (a) Water uses distribution; (b) Hourly water consumption profile through the day
hours а
s 3 •o
Time, hours b
Fig. 2. Variation of wind speed: (a) Speed on a Year; (b) Speed on a day to 10 m and 50 m above the ground
6
5
4
2
0
Table 1
Design variables
Design variables Nomenclature Range Component type considered
Wind turbine number NW 1-20 —
Tank number ^tank 1-10 —
Type of wind turbine T W 1-2 600 W - 1300 W
Type of tank T tank 1-2 20 m3-50 m3
Type of tower T lower 1-3 50 m - 60 m - 70 m
Type of well T head 1-3 30 m - 50 m - 70 m
the surplus of energy produced in expensive accumulators, this is the surpluses of pumped water which are stocked in a tank. Wind pumping system allows the conversion of mechanical energy into electrical energy through a rotor coupled to a generator, which controls the pump AC rated power 1000 W.
Wind turbine system model
Power output of wind turbine generator at a specific site depends on wind speed at hub height and speed characteristics of the turbine. Wind speed at hub height can be calculated by using power-law equation [15]:
of human activities. The daily water consumption of the tow is 30 m3/day (we have considered that it is the same for all the day in the year), and the hourly water consumption profile through the day is show in Figurelb. The proposed method is applied to a wind system designed to meet the daily water consumption needs of rural household. Data on wind speed from the meteorological station in Cotonou, located around thirty kilometers of the site selected in this work. In addition, these data are measured at 10 m from the ground and made an extrapolation using empirical models in the literature (Equation 1) to obtain the wind speed at 50 m above the ground. In Figure 2a are represented Hourly data of the wind speed at 10 m from the ground on one year and Figure 2b are represented Hourly data of the wind speed at 10 m and 50 m from the ground over one day.
The design variables needed to determine solutions are summarized in Table 1.
2. Description of the pumping system
To meet these needs, wind turbines can be used as an energy source for pumping water. The system used herein comprises a turbine, a water source, a water tank and a subsystem pumping (pump and motor) (see Fig. 3). For the systems of wind pumping operating over wind, the storage of water in the tanks is the solution most adopted compared to electrochemical storage in the batteries. Instead of storing
V2=VX
rz ^ 2
7
V i y
(1)
Where V and V2 are the wind speed at hub and reference height Z2 and Zx and a is roughness coefficient whose value generally varies between 0.1 and 0.25 depending on the site. The one-seventh power law (0.14) is a good reference number for relatively flat surfaces such as the open terrain of grasslands away from tall trees or buildings. Choosing a suitable model is very important for wind turbine power output simulations. The most simplified model to simulate the power output of a wind turbine [10] can be described by:
Pw =
P ■
v - V V - V
Pr 0
V < v < V
Vr < V < Vf V < V and V > V
(2)
f
where P is the rated electrical power; V is the cut-in wind
r i 7 c
speed; Vr is the rated wind speed; and Vf is the cut-off wind speed. The two turbines used in this study are of IMEX-Blade using Maglev technology. Their characteristics are summarized in Table 2.
Fig. 3. Configuration of a wind turbine powered pumping system
Table 2
Characteristics of the two wind turbine
Parameters Wind turbine 1 Wind turbine 2
P r 600 W 1300 W
Diameter 1.06 m 2 m
Height 1.20 m 2.1 m
V с 1 m/s 1 m/s
V 12 m/s 13 m/s
Vf 65 m/s 60 m/s
Where E, , is the maximum storage capacity
tank, max o i j
of the tank.
The functioning of tank is similar to that of a battery in an ordinary wind system. Thus, when the production of wind is sufficient water needs are satisfied and the rest of the energy is used to fill the tank. The water capacity of the tank is determined from the equation (5). In the case where the production of wind is not enough, the tank is loaded and its capacity is determined from equation (6).
Criteria for evaluating system performance
Pumping subsystems model
To determine the power of a submerged wells or drilling pump or surface pump, it is necessary to know the total head well as flow that we would like to tap. Thus, whereas in a wind pumping system, the required electrical power output to the motor-pump combination can be expressed as [4, 5, 9]:
P (t)=P^-L , (3)
iW 3600 h
where Q is the output water rate (m3/h), p is the density of water (kg/m3), g is the acceleration due to gravity (m/s2), 3600 is the number of second per hour, Ht is total head (m) and n is the power efficiency of the motor-pump combination.
The hourly consumption corresponding energy (Wh) of the pump is given by:
El (t ) = PL (t ) A T
К A t) = Elmi{t-\)+ Ew(t)-
EL{t)
Water storage discharging,
EL{t)
Л0
I conv /
-M0
0<E,ank(t)<EK
1. The economic model based on the LCC concept
Life cycle cost (LCC) includes the cost of initial investment, the cost of replacing the component, the cost of maintenance and repair and the cost of downtime. For a component of the system i, the economic cost of the life cycle (during 25 years) can be expressed by the following equation [7, 12, 14]:
LCC, = N, (CI, +CRX. +CMR,PWA(/r,Ä,)), With:
y> 1
J,
-1 If R is dividable to L
(4)
R
yi =~r If R is not dividable to L
L v •
Where AT is the simulation step that we take equal to 1 hour. Under these conditions, we equate power and energy.
Water storage tank model
The state of charge of a tank depends on wind production and water needs of users. Thus, the energy stored in the tank at a time t can be expressed by the following equation: Water storage charging,
PWA (ù , v )
= (1+ir)
Rv
1
ir (1 + ir )
Rv
(8)
(9)
(10) (11) (12)
■ (5)
(6)
Where Etank(f) and Etank(t-1) the energy stored in the tank (Wh) at the time t and t-1, are respectively; EW (t) is the total energy generated by wind turbines after energy loss of controller (Wh); EL (t) is the energy hydraulic demand at the time t (Wh); n and n , are the conversion efficiency
v vconv 'tank J
and charge efficiency of water storage tank, respectively, ntank is taken equal to 1. At any time t, the charged quantity of the water storage tank is subject to the following two constraints:
Where N. is number of component i, CI. is the initial investment cost, CR,. is the replacement cost, CMR,. is the cost of maintenance and repair of component i. PWA and K, are annual and single payment present worth factors, respectively; y, and L. are number of replacements of component i and its life time; ir is real interest rate, Rv is project's lifetime.
We then deduce the total economic cost of the life cycle of the system:
Ctotal =e LCCi . (13)
i
In this study, we chose ir = 6% and Rv = 25 years. The economic costs of the different components of the system are summarized in Table 3 [2, 12, 14, 18-21].
2. Gross energy requirement
The life cycle analysis is a tool for decision support in eco-design for evaluating the environmental impact of the system, from raw material extraction to end of life system. The indicator chosen in this study is the Gross energy requirement (GER). This cost represents the total primary energy required for the manufacture, maintenance, recycling and transport to the place of use of the system. For an autonomous wind system, the overall energy cost is as follows:
(7)
GERWo/ = NwPnGERwDVw +NmtE^№GERtMt yhl„kDVlal + P GER v DV +GER H.
n,conv conv у conv conv lower
(14)
Table 3
Components specification
Component CI CR CMR Efficiency (%) Life (yr)
Wind turbine 2 US$/W 2 US$/W 0.02 US$/W/yr — 25
Water tank 0.55 US$/m3 0.55 US$/m3 0.0055 US$/m3/yr 100 25
Motor pump 2.73 US$/W 2.73 US$/W 0.08 US$/W/yr 45 10
Converter 0.7 US$/VA 0.7 US$/VA 0.007 US$/yr 90 15
Tower 250 US$/m 250 US$/m 6.5 US$/m/yr — 25
Water drilling 0.27 US$/m 0.27 US$/m 0 US$/m — 25
Where GERM is primary energy cost of the system, GERr is primary energy cost, Pn is rated power, DVW is the life, of the wind. GERtank is primary energy cost, DVtank is the life, Ytank is number of replacements, of the water tank. GER is primary energy cost, DV is the life, Y is number
conv 1 J c'«/ ' conv 7 conv
of replacements, of the converter. GER and H are primary
A ' tower i J
energy cost and height of the mast, of the wind, respectively.
In relation (14) for lack of data, we have not considered the primary energy of the pump motor.
3. Life cycle CO2 emissions
Energy consumption during the implementation of the system generates CO2 emissions can also be evaluated as follows:
Where GESTotal is total CO2 emissions of system, GESr is CO emission from wind, GEs , is CO. emission from
2 ' tank 2
water tank, GES is CO emission from converter, GES
7 conv 2 7 tower
is CO2 emission from tower.
In relation (15) for lack of data, we did not take into account the CO2 emissions on the manufacture of motor pump.
Table 4 shows the calculation results for the energy consumption and CO2 emissions during system equipment manufacture. These are the numerical values per unit capacity per year [1, 11, 13, 18].
Table 4
Energy consumption and CO2 emissions in the system equipment manufacturing
in this study), the LPSP is the ratio of the sum of all values of energy loss LPS for the same period of the energy required. The loss of energy is expressed by [3]:
LPS is expressed by:
LPSP = XLPS (/)/iX(0 (17)
Models of the rates of satisfaction
The different criteria used in this study are not the same size. To solve this problem of scaling, desirability functions for transforming the variables dimensionless criteria are tapped. But the choice of a desirability function depends on the requirements of the study to be conducted in our case, all criteria are to minimize as shown in Table 6. For this purpose, the function of desirability of Harrington is used [16]:
d(Y.) = exp(-exp(P + «0) »ec „ = ,
| = ln (-In (0,99 ))-aUSL (18)
Where d is the desirability associated with the criterion Ym, AUC is the absolute upper cutoff, USL is the upper soft limit for the criterion. Levels of criteria are summarized in Table 5.
Table 5
Levels of criteria
Criteria Aim USL AUC
Components Facility energy CO2 emissions CI Minimize 100 50000
Wind turbine 0.215 kWh/W.yr 69 g CO2/W.yr CR Minimize 100 50000
Water tank 445 kWh/m3.yr 34000 g CO2/m3.yr CMR Minimize 418 800
Converter 0,4 kWh/VA.yr 12,5 g CO2/VA.yr LPSP Minimize 0 60%
Tower 7.2 kWh/m 5.9 g CO2/m GER Minimize 957766085 1.0246T09
GES Minimize 723597795 5.8365T09
4. Loss power supply probability
Because of the intermittent wind speed characteristics, which highly influence the energy production from the system, power reliability analysis is usually considered as an
important step in any such system design process. There
are a number of methods used to calculate the reliability of the systems. The most popular method is the loss of power
supply probability (LPSP) method. The design of a reliable
stand-alone wind system can be pursued by using the LPSP as the key design parameter. For an analysis period T (1 year
Then, the criteria are aggregated according the aggregation method based on weighted geometric mean of the functions of desirabilities [8]:
DOIt =f{d; (19)
r= 1
Where DOIk denote the indices of desirability and B the weights relating to the criteria. DOI1 is the index relating to the economic shutter, DOI2 is related to the reliability of the system, DOI3 is related to the environmental aspects.
Desirability indices obtained are aggregated according the same principle to lead to the global objective function:
OF = Х DOI
(20)
k=1
Where wk denote the weighting coefficients concerning index of desirability.
The weights used are essential because they represent the wishes of the user in the implementation of the wind system. The values of these weights are summarized in Table 6.
Table 6
Indices of desirabilities DOIj doi2 DOI3
Weight, % 22.55 67.38 10.07
Criteria DOI1 CI CR CMR
Weight, % 43.41 34.54 22.05
Criteria DOI3 GER GES —
Weight, % 60.99 39.01 —
Optimization method used
The optimization of the dimensioning of wind turbine system is a multi-objective optimization. Indeed, the cost of the system should be minimal while providing consumers with quality electricity supply the best possible. The number of variables is important, our choice fell on a genetic algorithm called NSGA-II («Nondominated Sorting Genetic Algorithm II») [6]. The main parameters of this algorithm are:
• Number of generations NG = 50;
• Number of individuals per generation N.nd = 100;
• Design variables (Table 1);
• Probability of crossover Pc = 0.80;
• Mutation probability Pm = 0.05;
The algorithm used to evaluate the performance of each individual by calculating the objectives, constraints specific to this individual and the global objective function after taking into account all the steps of the algorithm (crossover and mutation). In this study, six criteria are considered. These are:
• Minimization of all criteria under DOIj (CI, CR, CMR);
• Minimization of the criterion under DOI2 (LPSP);
• Minimization of all criteria under DOI3 (GER, GES).
Thus, for different sets of combination of design variables, we determine all the corresponding objective functions overall. 100 solutions candidates in total are obtained that we classify by decreasing order according to their corresponding rate of satisfaction. After modeling the problem in our approach to optimize multi-objective can be summarized as follows:
, N T T T T
W9 tank9 W9 tarh'
tank9 tower, head
Find x = [N,
Which minimizes OF (x ) = {CI (x) ,CR (x) ,...,GES (x)}; Subject to 100 < CI (x) < 50000; 100 < CR (x)< 50000; 723597795< GES(x) < 5.83 65 -109. (21)
1 -Nw <20 1<A^<10
1<T T <2 1 <T <3
L-1W> 1 tank- 1 -1 tower ~ J
1 < T < 3
1 — ^ head--
Thus, for different sets of combination of design variables, the corresponding global objective functions are determined. The candidate solutions obtained are ranked in descending order according to their corresponding satisfaction.
Results and Discussion
To check the status of operation of wind pumping system designed from models of the various constituent components, a simulation was achieved over three days. For this purpose a wind pumping system consisting of 20 turbines each rated power 1300 W, coupled to 10 tanks of rated capacity 50 m3 each is considered. The mast height is 70 m and the total head is 70 m. On Figure 4 (a), are superimposed the curves representing the load and the power produced by the entire wind turbine, respectively. From the observation of this figure, we see that the power produced by wind turbines is not regular and adjustable at will according to the needs of the user. For example, the maximum instantaneous power demand is 1272 W at 7 hours while the production of wind turbines is only 26 W at this precise moment. So the phase shift between wind power and water consumption does not favor the optimization of wind nor water autonomy.
As shown in Figure 4 (a), a significant proportion of wind power is not in line with the consumption. It is therefore necessary to add a wind system storage tanks in this case so that they can return the stored energy when the wind will not be able to cover the needs of the user. On Figure 4 (b), the variation of the charge state of the tanks a function of time well as the load and the power produced by wind turbines were simulated. The simulation was started with initially empty tanks. In times of strong wind (12:00 h to 19:00), wind turbines it possible to supply the consumer and fill the tanks. During periods of low wind (20:00 h to 30:00), wind power is insufficient and these are the tanks ensure the cover of the needs.
Figure 5, we selected the contours for which you want to display the value. At this optimal configuration corresponds 17 wind turbines rated power 600 W, 2 tanks of 20 m3 capacity, a mast height of 50 m and a total head 30 m ie a ratio of 255 W/m3. Figure 6 shows the relationship between the values of LPSP and different system configurations for different total head. At each value of LPSP a game of combination of design variables corresponds. In this part, the types of wind turbines, tank, and mast are set. Analysis of this figure reveals that more total head is greater, more it requires a large number of wind turbines and tanks. In addition, more the value of LPSP is low, more the number of wind turbines and of tanks is high.
Table 7 presents the five best solutions of the study well as their characteristics. These solutions satisfy the constraints of the problem and give results that minimize all the objectives defined in terms of three criteria while remaining within the scope of each decision variable. The first solution introduces a LPSP 7.52%. If we decide to cover all water needs (LPSP = 0%), it will use more wind turbines and tanks.
Fig. 4: Evolution of energy: (a) Called energy and energy produced by all the wind; (b) Variation of the charge state of the tank
0.7 0.6 0.5 0.4
4 5 6 7
Tank number
Fig. 5. Contours of the global objective function Conclusion
In this paper, we presented an optimization method to find the configuration optimal of a wind pumping system coupled to tanks. This system is designed to cover the water needs of a city of Benin. The components of the pumping subsystem are modeled and validated by simulation that it is not the most appropriate method. The genetic algorithm is used to make system optimization. The design of the pumping system is made according to the concept of the loss power supply probability (LPSP), the concept of the life cycle cost (LCC) and the concept of the life cycle energy of the system (primary energy and CO2 emissions). Different selected criteria are not the same size, the desirability functions are put to use to solve the problem of scaling.
At the end of this study, different candidate solutions are generated and made available to the design. The best solution obtained i.e. that which with the total objective function highest, consists of 17 wind turbines, 2 tanks, all type 1 (see table 1) a 50 m mast and a well pump head 30 m. This solution requires an LCC 38958 dollars, a primary energy of 963380185 kWh and a CO2 emission 1.165.109 with LPSP 7.52%; which corresponds to a ratio of 255 W/m3.
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Table 7
Characteristics of the ten best solutions
0.9
0.8
0.3
0.2
0.1
2
3
8
9
0
No nw Ntank T w T,ant Ttower Thead CI RC MRC GER GES LPSP,% OF
1 17 2 1 1 1 1 34546 3803 609.32 963380185 1.165x109 7.52 0.9512
2 6 2 2 1 1 1 29746 3803 561.32 963367285 1.161x109 16.38 0.9424
3 15 3 1 1 3 2 37159 3803 715.43 968936379 1.588x109 6.27 0.9419
4 13 1 1 1 2 1 32235 3803 626.21 957804857 736017854 16.11 0.9403
5 14 7 1 1 2 2 33503 3803 638.87 991183082 3.2871x109 4.43 0.9390
1300 W - 50 m3 - 70 m - 30 m
1300 W - 50 m3 - 70 m - 30 m
Wind turbi
0.8-г 0.6 So 0.4-
□L
0.2-
Wind turbine
1
0.8 0.6 0.4 0.2
Wind turbine
Tank number
1300 W - 50 m3 - 70 m - 70 m
1300 W - 50 m3 - 70 m - 50 m
9 10
1300 W - 50 m3 - 70 m - 70 m
4 Tank number
0.6 0.5
Fig. 6: Visualization of LPSP: (a) 3 D representation of LPSP; (b) Contours LPSP
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0.7
0.8
0.6
0.6
0.4
0.2
0.1
12345Ö/Ö Tank number
0.7
0.1
00
2U
0.8
0.7
0.4
0.3
U.2
0.1
00
2
3
45
67
8
9
Статья поступила в редакцию 10.02.2015
