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DOI: 10.32604/EE.2021.017464
ARTICLE
Optimal Conguration of an Off-Grid Hybrid Wind-Hydrogen Energy
System: Comparison of Two Systems
Zekun Wang1,2,4,YanJia
1,2,3,*, Yingjian Yang1, Chang Cai4,5 and Yinpeng Chen1
1School of Energy and Power Engineering, Inner Mongolia University of Technology, Hohhot, 010051, China
2Key Laboratory of Wind Energy and Solar Energy Technology (Inner Mongolia University of Technology),
Ministry of Education, Hohhot, 010051, China
3Inner Mongolia Autonomous Region Wind Power Technology and Testing Engineering Technology Research Center,
Inner Mongolia University of Technology, Hohhot, 010051, China
4Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100190, China
5Key Laboratory of Wind Energy Utilization, Chinese Academy of Sciences, Beijing, 100190, China
∗Corresponding Author: Yan Jia. Email: jia-yan@imut.edu.cn
Received: 12 May 2021 Accepted: 28 July 2021
ABSTRACT
Due to the uncertainty of renewable energy power generation and the non-linearity of load demand, it
becomes complicated to determine the capacity of each device in hybrid renewable energy power generation
systems. This work aims to optimize the capacity of two types of the off-grid hybrid wind-hydrogen energy
system. We considered the maximum prot of the system and the minimum loss of power supply probability
as optimization goals. Firstly, we established steady-state models of the wind turbine, alkaline electrolyzer,
lead-acid battery, and proton exchange membrane fuel cell in matrix laboratory software to optimize the
capacity. Secondly, we analyzed the operating mode of the system and determined two system structures
(system contains batteries whether or not). Finally, according to the wind speed and load in the sample
area, we compared the economics of the two systems and selected the optimal conguration for the area.
In the same calculation example data, the non-dominated sorting genetic algorithm-II (NSGA-II) is used
to optimize the capacity of each device in the two systems. The results showed that the prot of the without
battery-equipped system is 32.38% higher than another system. But the power supply reliability is the
opposite. To avoid the contingency of the calculation results, we used the traditional genetic algorithm
(GA) and ant colony optimization (ACO) to calculate the same example. The results showed that NSGA-II
is signicantly better than GA and ACO in terms of iteration steps and calculation results. The required
architecture for the System-I composes of 3 numbers of 10 kW wind turbines, 61 sets of 12 V·240 Ah lead-
acid batteries, 8 kW electrolytic cell, and 6 kW PEMFC. The net prot and LPSP are 44,315 and 0.01254
respectively. The required architecture for the System-II composes of 2 numbers of 10 kW wind turbines,
24 kW electrolytic cells, and 18 kW PEMFC. Net prot and LPSP are 58,663 and 0.03244, respectively.
This paper provided two schemes for the optimal conguration of the hybrid wind-hydrogen energy system
in islanding mode, which provided a theoretical basis for practical engineering applications.
KEYWORDS
Optimization; wind energy; hybrid energy system; off-grid; fuel cell
This work is licensed under a Creative Commons Attribution 4.0 International License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
1642 EE, 2021, vol.118, no.6
Nomenclature
DC Direct current
Qtank Volume of the hydrogen storage tank
AC Alternating current
QAE,THydrogen produced by electrolyzer during T period
vrated Rated wind speed of wind turbine
QFC,THydrogen consumption of PEMFC during T period
v(t)Wind speed at time t
ηtEfciency of storing hydrogen
vin Cut in wind speed
ηPEM Conversion efciency of PEMFC
vout Cut out wind speed
ηAE Electrolysis efciency of alkaline electrolyzer
vWWind speed at the height of the wind turbine hub
NAE Capacity of the alkaline electrolyzer
vHWind speed measured at height HH
Nhst Actual hydrogen storage
PW(t)Power output of wind turbine at time t
Rnet Net prot of the system
Pbat−c(t)Charging power of the battery at time t
RH2,TAnnual sales revenue of hydrogen during T period
Pbat−in(t)Input power of the battery at time t
REN Environmental benets during T period
Pbat−f(t)Discharging power of the battery at time t
C0Average annual cost
Pbat−out(t)Output power of the battery at time t
CNHydrogen storage tank capacity per unit
PAE Rated power of alkaline electrolyzer
CTCost of the whole life cycle
Pnet Net power of the system
CCCost of initial purchase
Pex Excess electricity in the system
CMCost of operation and maintenance
PPEM Output power of PEMFC
CRCost of replacement
P0Rated power of wind turbine
Rnet Net prot of the system
PBN Rated power of the battery
SH2Selling price of hydrogen
PFN Rated power of PEMFC
VNOutput voltage of alkaline electrolyzer
PL(t)Load demand power at time t
HWThe height of the wind turbine hub
QHydrogen volume
NAAvogadro constant
Qnet Net energy accumulation
SOCmax Maximum SOC of the battery
QtEquivalent chemical energy of Qvolume hydrogen
SOCmin Minimum SOC of the battery
Qin Amount of hydrogen input
EE, 2021, vol.118, no.6 1643
iAnnual interest rate
QNRated hydrogen production rate of alkaline electrolyzer
r0Hydrogen compression ratio
Q0Rated capacity of the battery
yLife of the equipment
1 Introduction
In recent years, people have developed a strong interest in the application of renewable
energy. The main reason is that the traditional fossil energy reserves are limited, and the energy
market is unstable [1,2]. On the other hand, it is due to the increasing environmental pollu-
tion [3]. Moreover, the unlimited nature of renewable energy is very benecial to future energy
development.
At present, it is urgent to solve the problem of energy waste caused by the long-distance
transmission of electricity to remote areas [4]. It is also showed the importance of off-grid
renewable energy power generation systems. Wind energy, due to its low pollution and cost, is
currently one of the main ways to change the world’s environment and energy problems [5,6].
It is of great signicance to improving the global energy structure and reducing electricity costs.
Nowadays, people have paid great attention to the construction of hybrid renewable energy power
generation systems [7–9].
However, the shortcomings of wind power generation such as power uctuation and output
intermittent, have also emerged [10]. The hydrogen storage system has the characteristics of fast
charging (discharging) and large capacity [11–13]. It is used in conjunction with wind turbines
to effectively solve the uctuation and intermittent problems of wind power generation. What is
more, it can improve the reliability and safety of the system power supply. The hybrid energy
system composed of electrolyzer and batteries or fuel cells has complementary advantages [14].
It is used to smooth the volatility of the output power and has technical and economic benets.
It is worth noting that the capacity of the storage system will affect the cost of the power
generation system [15]. Therefore, the economic optimization of off-grid renewable energy power
generation systems has become a research focus. Wu et al. [16] used the hybrid iteration-adaptive
hybrid genetic algorithm (HIAGA) to calculate the objective function of life cycle-net present
cost (NPC). They calculated the optimal capacity ratio between wind turbines, photovoltaic
(PV) arrays, and battery installations. In [17], Chen et al. used an adaptive genetic algorithm
(AGA) to optimize the installation capacity of a stand-alone hybrid wind-solar generation system.
In [18], they used the hybrid optimization model for electric renewables (HOMER) software to do
the simulations and perform the techno-economic evaluation for a standalone hybrid solar-wind
system with battery energy storage for a remote island. It is the early hybrid renewable energy
power generation system (hybrid wind-solar generation system). Subsequently, more and more
scholars try to add other energy sources to the power generation unit. In [19], they used the
genetic algorithm to optimizing and analyzing a stand-alone PV-wind-battery-diesel hybrid system
to meet the electricity needs of Fanisua. Li et al. [20] modelled and optimized in HOMER for
different combinations of PV panels, wind turbine, and biogas generator. In [21], they used the
ower pollination algorithm to optimize the conguration of off-grid solar photovoltaic fuel cell
(PV/FC) hybrid systems. Moreover, they compared with the articial bee colony algorithm and the
particle swarm optimization. The advantage of solar power generation is that it can compensate
for the intermittent nature of wind power generation. However, as mentioned in [22], solar power
still harms the environment. In recent years, the cost of solar power generation has declined [23],
1644 EE, 2021, vol.118, no.6
but solar energy is still in the ranks of high-cost energy. Also, the safe operation of solar power
generation needs to be improved. Therefore, this paper is aimed at hybrid energy systems operated
in islanding mode and did not consider added solar power generation.
The improvement of energy storage systems has also become one of the research hotspots.
In [24], they took two types of electrochemical batteries (Lithium Nickel Manganese Cobalt
Oxide; and PbO2-Lead-Acid Battery) into a hybrid generation system for energy storage. In [25],
they considered three different battery technologies in hybrid generation system, including
Flooded Lead Acid (FLA), Lithium Ferro Phosphate (LFP), and Nickel Iron (Ni–Fe). Nowadays,
more and more scholars pay attention to the advantages of high utilization rate and convenient
storage of hydrogen energy storage. References [26–28] used an electrolyzer and hydrogen storage
tank in a hybrid renewable energy power generation system to store excess electricity. The fuel cell
consumed hydrogen energy to generate electricity when the output power of the power generation
unit cannot meet the power demand of the load.
At present, scholars from all over the world have optimized the hybrid energy system in
different research directions. As far as the economic optimization of the system is concerned, the
goal is to minimize the total cost of system operation or maximize the prot based on meeting
the load demand [29,30]. But for a region that has never established an integrated energy system,
we need to determine which system is suitable for the region through simulation calculations.
Therefore, we need to compare the economics of different systems when other conditions are the
same. Through the comparative analysis of the results, we can provide options for future system
construction. This is also the signicance of this study.
This work aims to optimize the capacity of the two kinds of hybrid wind-hydrogen energy
(HWHE) system in islanding mode, considered the maximum prot of the system and the
minimum loss of power supply probability. Firstly, we established steady-state models of the wind
turbine, alkaline electrolyzer, lead-acid battery and proton exchange membrane fuel cell in matrix
laboratory software to optimize the capacity. Secondly, we analyzed the operating mode of the
system and determined two system structures (the system contains batteries whether or not).
Finally, according to the wind speed and load data in the calculation example area, the annual
power generation of the system is estimated with the loss of power supply probability as the
constraint condition. In the same calculation example data, the non-dominated sorting genetic
algorithm-II (NSGA-II), genetic algorithm (GA) and ant colony optimization (ACO) is used to
optimize the capacity of each device in the two systems.
The contribution of this study is as follows: i) Because of the optimization of a single
system in the current research, this paper used two systems for comparison. ii) Through the
analysis of the calculation results and calculation speed of NSGA-II, GA, and ACO, NSGA-
II has shown good adaptability in the optimization of the HWHE system. iii) To compare the
nal optimization results, we analyzed the advantages and disadvantages of the two systems. It
provided a reference for actual construction in the future. This study is organized as follows.
Section 2 introduced the structure of the HWHE system and the mathematical model of the
main components. Section 3 introduced the optimized algorithm and economic modeling. In the
fourth section, a case study in Northwest China is simulated and veried. Section 5 summarized
the conclusion.
2 Description of the HWHE System
In this section, we introduced the structure of two kinds of wind-hydrogen hybrid energy
systems. Besides, we established mathematical models of the main components.
EE, 2021, vol.118, no.6 1645
2.1 Structure of the HWHE System
In this paper, we proposed two kinds of HWHE systems (System I & System II). The
common feature of the two system structures is that they both contain a wind turbine, alkaline
electrolyzer, hydrogen storage tank, PEMFC, inverter and rectier. The difference is that System
I contain lead-acid batteries. The structure diagram of the two systems is shown in Fig. 1.
Figure 1: (A) System-I (B) System-II
The whole system consists of three parts: power generation, power storage and power con-
sumption. In this paper, wind energy is the source of power generation. In the System I, lead-acid
batteries work as energy storage to regulate and balance the load. After meeting the load demand,
the excess power rst enters the battery and then enters the electrolyzer. The function of the
battery is to suppress uctuations in the output power of wind power generation. However, the
System I with the battery will reduce the capacity and cost of the hydrogen storage unit. Unlike
the System I, the excess electricity generated in System II will directly enter the hydrogen storage
unit. The power consumption in the load, divided into two types: DC load and AC load [31].
Considering the actual construction situation, DC bus and AC load have been used in the system.
2.2 Wind Turbine
The wind power generation system is mainly composed of a wind turbine and generator.
The output power of a wind turbine is closely related to factors such as wind speed and blade
material. In this study, we only considered the impact of wind speed on the output power of wind
turbines. There are two parameters index dening wind speed, rated wind speed and boundary
wind speed. The boundary wind speed mainly refers to the cut-in wind speed and the cut-out
wind speed. When the actual wind speed is greater than the cut-in wind speed, the wind turbine
begins running. The rated wind speed is between the cut-in wind speed and the cut-out wind
speed, corresponding to the rated power. When the actual wind speed is greater than the rated
wind speed but less than the cut-out wind speed, the wind turbine supplies energy with the rated
power. To ensure the sunit’s safety, the wind turbine will stop running when the actual wind speed
1646 EE, 2021, vol.118, no.6
is greater than the cut-out wind speed. The mathematical model is shown in Eq. (1) [32].
PW(t)=
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
0v(t)<vin
P0×v(t)−vin
vrated −vin
vin ≤v(t)≤vrated
P0vrated ≤v(t)≤vout
0v(t)>vout
(1)
It is worth noting that the height of the wind measurement tower is usually different from
that of the wind turbine hub. So, we need to use the power function method to simulate the
vertical distribution of wind speed. It can be calculated by the Eq. (2) [33].
vW
vH=HW
HHθ
(2)
where θis the coefcient of the wind speed energy law. It is affected by many factors such
as altitude and season. In this study, we take the reference value 1/7, which under at ground
condition.
2.3 Lead-Acid Battery
The batteries are used in the system to improve the balance of power supply and demand.
Its capacity is determined by the remaining power of the battery and the state of charge and
discharge. The performance of the battery is evaluated by the instantaneous balance equation
of the state of charge (SOC). The power of charging and discharging is shown in the Eqs. (3)–
(4) [34].
Pbat−c(t)=Pbat−in(t)×ηbat−in =dSOC
dt (3)
−Pbat−f(t)=Pbat−out(t)×ηbat−out =dSOC
dt (4)
According to the working state of the battery, its mathematical model can be divided into
four situations.
Case 1. The output power of the wind turbine is greater than the demand of the load, and
the battery starts to charge. However, the capacity of the battery does not reach the maximum
value of SOC. The state of charge of the battery at time t is as Eq. (5).
⎧
⎨
⎩
SOC(t)=(1−δ)SOC(t−1)+Pbat−in(t)×t×ηbat−in
Q0
Pbat−in(t)=Pex
(5)
Case 2. The output power of the wind turbine is greater than the demand of the load, and
the battery starts to charge. The capacity of the battery has reached the maximum value of SOC.
EE, 2021, vol.118, no.6 1647
However, there is still excess power. The state of charge of the battery at time t is as Eq. (6).
⎧
⎨
⎩
SOC(t)=SOCmax
Pbat−in(t)=[SOCmax −SOC(t−1)]×Q0
t
(6)
Case 3. The output power of the wind turbine is lower than the demand of the load, and
the battery starts to discharge. The capacity of the battery has not been reduced to the minimum
value of SOC. The state of discharge of the battery at time t is as Eq. (7).
⎧
⎨
⎩
SOC(t)=(1−δ)SOC(t−1)−Pbat−f(t)t
Q0ηbat−out
Pbat−f(t)=Pex
(7)
Case 4. The output power of the wind turbine is lower than the demand of the load, and
the battery starts to discharge. The capacity of the battery has reduced to the minimum value of
SOC. At this time, the batteries stop discharging. The state of discharge of the battery at time t
is as Eq. (8).
⎧
⎨
⎩
SOC(t)=SOCmin
Pbat−f(t)=[SOC(t−1)−SOCmin ]×Q0
t
(8)
where ηbat−in is the charging efciency of the battery; ηbat−out is the discharge efciency of the
battery; δis the self-discharge rate of the battery; tis the operating time of the battery.
2.4 Alkaline Electrolyzer
Hydrogen production by water electrolysis is a convenient way. The tank body lled with
electrolyte is divided into anode suffocation and cathode suffocation by a diaphragm, and cor-
responding electrodes are placed in each chamber. At present, there are many studies on the
application of acidic electrolyzer and alkaline electrolyzer in hybrid energy systems. Although the
efciency of an acidic electrolyzer is higher than that of an alkaline electrolyzer, its cost is higher.
Therefore, the alkaline electrolyzer is used in the system proposed in this paper. The reaction
equations of the anode and cathode are as follows [35]:
4OH−→O2+2H2O+4e−
2H2O+4e−→O2+4H+⇒2H2O→O2+2H2(9)
According to Faraday’s laws of electrolysis, the amount of gas produced by the electrolysis of
water is proportional to the direct current. The mathematical model of the alkaline electrolyzer
and hydrogen storage tank is as follows:
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
PAE =2QNNAVN
3600VmC0ηAE
Q=PtQN
PAE
NAE =max Pnet
PAE
(10)
1648 EE, 2021, vol.118, no.6
where Vmis the molar volume of gas at room temperature and pressure; C0is the number of
electrons per coulomb; Ptis the equivalent power of Qvolume hydrogen.
For the hydrogen storage tank, we need to consider its actual hydrogen storage capacity. We
ignored the inuence of temperature on hydrogen storage.
Nhst =max Qnet
Pt
,Qnet =QtPAE
r0C0
(11)
2.5 PEMFC
The fuel cell is based on hydrogen fuel and uses the principle of a redox reaction to convert
the chemical energy in hydrogen fuel into electrical energy. PEMFC has the characteristics of low
operating temperature, low noise and high power etc. It is suitable for hybrid energy systems. The
PEMFC consists of cathode, anode and proton exchange membrane. The reaction equations of
the anode and cathode is as follows [36]:
2H2→4H++4e−
O2+4H++4e−→2H2O⇒2H2+O2→2H2O(12)
For the reaction process of PEMFC, the mathematical model can be expressed as the reverse
process of electrolysis of water. We can use the Eq. (13).
PPEM =2QinNAVNηPEM ηt
3600VmC0
(13)
3 Optimized Algorithm and Economic Modelling
In this section, we introduced the optimization algorithm, optimization objectives and con-
straints used in this research. The main optimization goal is the highest prot for the whole life
cycle of the system. Besides, we also required that the loss of power supply probability does not
exceed the maximum allowed.
3.1 The Non-Dominated Sorting Genetic Algorithm-II (NSGA-II)
For multi-objective optimization problems, genetic algorithm, particle swarm algorithm,
NSGA-II, etc., are all applied. In a multi-objective optimization problem, multiple goals will
inuence each other. In other words, when the value of one target is increased, the other target
may decrease. Therefore, we cannot achieve the optimal value of all the goals. NSGA-II was
proposed by Kalyan-moy Deb in 2002. Unlike other algorithms, the NSGA-II provides a method
to adjust the parameters between objects to achieve the best integration of the objective function.
The calculation of NSGA-II can be roughly divided into three stages [33,37,38].
STAGE 1: The population is stratied according to the non-inferior solution level of the
individual. Individuals at the same level have the same non-dominated order i0. Its purpose is to
direct the search direction to the optimal Pareto solution set.
STAGE 2: NSGA-II adds individual crowded distance to it. Its purpose is to selectively sort
individuals on the same level. In the calculation process, priority is given to selecting individuals
with a crowded distance. This operation can make the calculation results evenly distributed in the
target space, ensuring the diversity of the group.
STAGE 3: Keep the high-quality individuals in the parent directly into the offspring. Its
purpose is to prevent the loss of the optimal solution that has been obtained.
Solving process of NSGA-II is shown in Fig. 2.
EE, 2021, vol.118, no.6 1649
Figure 2: Solving process of NSGA-II
3.2 Optimization Goals and Constraints
3.2.1 Optimization Goals
In this paper, we considered the benets of renewable energy generation to the environment
and the time value of funds. The system economic model is established with the goal of prot
maximization.
1650 EE, 2021, vol.118, no.6
The cost of the system mainly includes the initial investment cost, replacement cost and
maintenance cost. The income mainly includes hydrogen sales prot and environmental benets.
The subtraction of the two is the net prot of the system. The mathematical model is shown in
the Eq. (14) [39].
MAXRnet =
n
T=1
(RH2,T+REN,T)−C0(14)
RH2,T=(QAE,T−QFC,T)×SH2(15)
REN =
n
X=1
[(λX+μX)×MX] (16)
C0=CT×i(1+i)y
(1+i)y−1(17)
CT=
n
T=1
[(CCW +CRW +CMW )PW,T+(CCB +CRB +CMB)PB,T+(CCA +CRA +CMA)PA,T
+(CCF +CRF +CMF )PF,T]
(18)
Note: When calculating the cost of System-II, the underlined part should be deleted.
where λXis the environmental value of the Xth pollutant; μXis the penalty level of the Xth
pollutant; MXis the annual reduction in emissions of type X pollutants caused by wind
power generation; CTis the cost of the life cycle of the system; CC∗,CR∗,CM∗is the initial
construction cost of each component; subscript W,B,A,Fis a wind turbine, lead-acid battery,
alkaline electrolyzer and PEMFC; P∗,Tis the output power of each component at time T.
To optimize of wind-hydrogen hybrid energy storage systems operating in island mode, the
loss of power supply probability (LPSP) is also an important optimization goal [40,41]. The load
demand must be met rst, and then prot maximization can be considered. The power reliability
of the off-grid HWHE system is measured by the indicator of LPSP. To accurately show the
operation of the system, this study used the time sequence method to characterize the LPSP. It
is dened as the ratio of system power outage time to power supply time.
LPSP =
r
t=0
T{[PW(t)+PPEM (t)]<PL(t)}
Tt
(19)
3.2.2 Constraints
The initial assumptions of the system conguration are based on the following constraints.
EE, 2021, vol.118, no.6 1651
Considering the construction cost of wind farms, the scale of installed wind turbine capacity
is determined according to load demand. The construction number of each piece of equipment
should satisfy the Eq. (20).
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
0<NW<P
P0
0<NB<P
PBN
0<NF<P
PFN
(20)
In the System I, the SOC of the battery at time t should not exceed the upper limit or fall
below the lower limit [42]. Refer to the operating instructions of the lead-acid battery; we set up
SOCmax =0.8, SOCmin =0.2.
SOCmin ≤SOC(t)≤SOCmax (21)
The LPSP should be lower than the maximum allowable value, which was set to 0.05 in this
paper.
LPSP(t)≤LPSPmax =0.05 (22)
The net hydrogen production at time T should be less than the volume of the hydrogen
storage tank.
QAE,T−QFC,T≤Qtank (23)
4 Case Study
In order to verify the feasibility of the proposed method, the optimization scheme is realized
by programming in MATLAB. Based on the above model analysis, the wind resource parameters
in Ulanqab, Inner Mongolia Autonomous Region, China (N 42◦11267, E 112◦28308)in
2020 were selected as the calculation example. The wind speeds every 10 min is measured at a
local height of 50 m. We used MATLAB to convert it to an hourly average (as shown in Fig. 3).
Figure 3: Hourly wind speed in 2020
1652 EE, 2021, vol.118, no.6
We selected the hourly average load of the village in the study area for 24 h. Then we
expanded the data for one day by 365 copies, and the load demand of 8760 h is shown in
Fig. 4. It was worth noting that we ignored the real-time uctuation of the load demand and
only calculated the average value. Because real-time monitoring of load changes is beyond our
scope of work. Moreover, this detail will not affect our results.
Figure 4: Average load demand per hour of one day
In this study, we chose FD-type wind turbines with a rated power of 10 kW. The rated wind
speed is 10 m/s, the cut-in wind speed is 3 m/s, and the cut-out wind speed is 22 m/s. Chose a
lead-acid battery with a rated capacity of 240 Ah and a rated voltage of 12 V. The parameters of
the main components in the system are shown in Tab. 1. In terms of algorithm, the maximum
number of iterations is set to 100. The initial population is 200. The crossover probability is 0.8.
The mutation probability is 0.01.
Table 1: The economic parameters of each component in the system (Chinese yuan-CNY, )
Components Capacity CC/CNY CM/CNY CR/CNY Life/year
Wind turbine 10000 W 76300 49500 0 20
Lead-acid battery 12 V·240 Ah 1500 3100 4900 5
Alkaline electrolyzer 8000 W 50880 9600 0 20
PEMFC 6000 W 18900 8280 0 20
To avoid the contingency of results caused by using a single algorithm. This study used
GA and ant colony optimization (ACO), which frequently appear in multi-objective optimization
problems. Moreover, we compared the calculation results of three algorithms. We have selected
three groups among the many solutions of each algorithm, and got the nal optimization result.
The optimization results are shown in Tab. 2.
The SOC of the battery will affect its working life, thereby reducing the net prot of the
system. The SOC of the lead-acid batteries for 8760 h throughout the year is shown in Fig. 5.
EE, 2021, vol.118, no.6 1653
Table 2: The optimization results of NSGA-II, GA and ACO
Algorithm Type NWNBNAE NFLPSP Rnet/CNY Optimal result
NSGA-II System-I 2 96 1 1 0.01574 49,613
3 79 1 1 0.01941 42,241
3 61 1 2 0.01254 44,315 √
System-II 2 0 2 3 0.03640 61,231
2 0 3 3 0.03244 58,663 √
3 0 4 3 0.02281 41,024
GA System-I 3 106 1 2 0.01846 39,858
2 99 1 1 0.02151 42,509
2 85 1 2 0.01547 38,330 √
System-II 2 0 2 4 0.03147 50,214
3 0 2 3 0.02816 48,190 √
3 0 3 4 0.02140 39,474
ACO System-I 3 98 2 1 0.01744 43,110
3 139 1 1 0.01564 39,912 √
2 108 1 2 0.01399 36,100
System-II 3 0 2 3 0.02441 46,320
2 0 3 3 0.03315 50,147 √
2 0 3 4 0.02915 43,228
Figure 5: SOC of a lead-acid battery in 8760 h (NSGA-II)
In the whole year of 8760 h, the SOC of lead-acid battery uctuates between 0.2–0.8, which
is safe. This can protect the battery to the utmost extent and avoid the increase in system cost
caused by frequent battery replacement. In addition, SOC has a relatively long time in 0.8. This
means that the battery is in a sufcient state for a long time, guaranteeing the load demand to
the greatest extent.
The iterative process curves of the three algorithms are shown in Fig. 6.
1654 EE, 2021, vol.118, no.6
Figure 6: Iteration process curve of NSGA-II GA and ACO. (A) System-I (B) System-II
We can get the optimal conguration of the HWHE system by comparing the above opti-
mization results. This study used three algorithms to compare the two systems. However, the
calculation results showed that each has its advantages and disadvantages. So we need to discuss
this deeply. In terms of algorithms, the calculation speed of NSGA-II is signicantly better than
GA and ACO. In the optimization process of System-I, NSGA-II converges in about 43 steps,
while GA and ACO require 55 and 80 steps, respectively. In the optimization process of System-II,
NSGA-II converges at about 38 steps, while GA and ACO require 60 and 74 steps, respectively.
In terms of calculation results, the nal prot of NSGA-II is higher than that of GA and ACO.
The optimization result of NSGA-II for System-I is 44,315, which is 15.61% and 11.03% higher
than GA and ACO, respectively. NSGA-II’s optimization result for System-II is 58,663, which
is 21.73% and 16.98% higher than GA and ACO, respectively.
By comparing the optimization results of the three algorithms, we found that the prot of
System-II is higher than that of System-I. However, it is worth noting that the LPSP of System-I
is generally lower than that of System-II. In other words, System-I is more reliable than System-
II. In summary, NSGA-II has more advantages in optimization depth, optimization speed, and
solution stability in optimizing the HWHE system. As for the choice of the system, System-II has
higher prots, but its reliability has deteriorated, while System-I is the opposite. Therefore, the
research personnel should fully consider the joint inuence of net prot and LPSP in selecting
the system. The required architecture for the System-I composes of 3 numbers of 10 kW wind
turbines, 61 sets of 12 V·240 Ah lead-acid batteries, 8 kW electrolytic cell, and 6 kW PEMFC.
EE, 2021, vol.118, no.6 1655
The net prot and LPSP are 44,315 and 0.01254, respectively. The required architecture for the
System-II composes of 2 numbers of 10 kW wind turbines, 24 kW electrolytic cells, and 18 kW
PEMFC. Net prot and LPSP are 58,663 and 0.03244, respectively.
5 Conclusion
Wind energy is one of the renewable energy sources which has been widely used. However,
the uncertainty of its power generation and the nonlinearity of load demand make it very
complicated to determine the capacity of each device in the hybrid renewable energy power
generation system. HWHE system has advantages in compared with independent wind power
generation systems. This paper took the area of Northwest China as an example and proposed
two kinds of HWHE systems. In the absence of grid power, the hybrid system supplies power
to the area. Firstly, we established steady-state models of the wind turbine, alkaline electrolyzer,
lead-acid battery and PEMFC in MATLAB to optimize the capacity. Secondly, we analyzed
the operating mode of the system and determined two system structures (the system contains
batteries whether or not). Finally, we compared the economics of the two systems and selected
the optimal conguration for the area according to the wind speed and load in the sample area.
In the same calculation example data, the non-dominated sorting genetic algorithm-II, genetic
algorithm and ant colony optimization is used to optimize the capacity of each device in the two
systems. As a result, NSGA-II’s optimization result for System-II is 21.73% and 16.98% higher
than GA and ACO, respectively. The optimization result of NSGA-II for System-I is 15.61% and
11.03% higher than GA and ACO, respectively. Besides, the cost of a battery-equipped system is
32.38% higher than another system by NSGA-II. As for the choice of the system, System-II has
higher prots, but its reliability has deteriorated, while System-I is the opposite. Therefore, the
research personnel should fully consider the joint inuence of net prot and LPSP in selecting the
system. This article provided the theoretical basis and data support for decision-makers to design
HWHE system. And also promoted the development and construction of off-grid integrated
energy systems.
Acknowledgement: We would like to thank all those who have reviewed and contributed to this
paper for their valuable assistance.
Funding Statement: This work was supported by the Inner Mongolia Science and Technology
Program under Grant 2021GG0336, and by the Open Fund of Key Laboratory of Wind Energy
and Solar Energy Technology (Inner Mongolia University of Technology), Ministry of Education
(No. 2020ZD01) in China.
Conicts of Interest: The authors declare that they have no conicts of interest to report regarding
the present study.
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