Optimization of solar thermal power station LCOE based on NSGA-II algorithm

LU Xiao-juan, LI Xin-yang， DONG Hai-ying

(1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University， Lanzhou 730070, China;2. School of New Energy and Power Engineering, Lanzhou Jiaotong University， Lanzhou 730070, China)

0 Introduction

Energy and environment are the foundation of human survival, which are facing the growing shortage of fossil energy today, the exploitation and utilization of solar energy resources will be the ultimate solution to the sustainable development of energy resources in the world[1]. According to the “13th Five-Year Power Development Plan” issued by the National Development and Reform Commission and the National Energy Administration, by 2020, China’s non fossil power generation installed capacity can reach 770 million kW, of which solar thermal power generation installed capacity is about 5 million kW[2]. At present, the solar thermal power generation system is mainly divided into two systems: point focus and line focus. The linear focusing system mainly consists of concentrator, collector, heat storage device and power generation device[3]. Linear Fresnel solar power generation system has received extensive attention due to its simple structure, low cost, good wind resistance and other characteristics when it needs to be installed in a large area[4].

Due to the large scale, high power generation and huge initial investment of solar thermal power station, the optimization analysis of unit generation cost is of great significance. In 2015, Li X et al. analyzed the generation cost of tower solar power generation system, but the modelling process was not given in his paper[5]. In 2013, the collector performance and the generation cost of solar parabolic trough thermal power generation were studied by Geng L S, and suggestions for reducing the cost were also put forward, however, the impact of scale effect on the system was not considered in the paper[6]. At the same year, the study of the cost and performance of solar thermal power generation system with a heat storage system by Nithyanandam K shows that when the capacity of the power station is large enough, the heat storage system can obviously reduce the cost of power generation and improve the reliability of the system[7]. Although there are many researches on solar thermal power generation in the world, the research and prediction of the generation cost of linear Fresnel solar thermal power generation system are still rare.

For the linear Fresnel solar power generation system, the research focuses of this paper are as follows: (1) establish the system capacity and levelling cost of energy (LCOE) model; (2) make a comparison between the multi-objective optimization algorithm NSGA-II and particle swarm optimization, and then analyse the results of the two algorithms on the system optimization; (3) the LCOE of linear Fresnel solar thermal power generation system is optimized by using non-dominated sorting genetic algorithm II (NSGA-II), the results show that due to the scale effect of solar thermal power generation, the larger the power station is, the lower the LCOE is, and the influence of thermal storage and loan on LCOE is also compared.

1 Optimization model of solar thermal power generation system

1.1 Capacity modeling of solar thermal power generation system

Solar thermal power plant mainly consists of two parts: solar collector and generator. Solar energy collector tracks the sun position by solar tracking device, receives and focuses the solar energy, heats the heat medium inside the heat collecting tube, thereby converting the solar energy into heat energy. The solar radiation energy absorbed by the collector is expressed by

Qu=Gscos(θ)fθfsfeηefo,

(1)

whereGis the direct normal irradiance (DNI), W/m2;sis the collector area, m2;θis the solar incidence angle;fθis the correction factor of solar incidence angle. According to Ref.[8], the correction methods of the LS-2 solar collector incident angle are

(2)

K=cosθ+0.000 884θ-0.000 053 69θ2,

(3)

(4)

cosθz=sinφsinδ+cosφcosδcosω.

(5)

So the correction factor of the incidence angle of solar collector is

(6)

whereθzis the zenith angle;φis latitude;ωis hour angle;δis deflection angle.

In Eq.(1),fsis the shading loss impact factor of solar collector, which can be concluded by

(7)

whereLsis the solar collector spacing, m；Wis the solar collector opening spacing, m.

And,feis the impact factor of end loss in heat collecting tube， which can be expressed by

(8)

wherefis the solar collector focus, m;Lscais the length of a single collector, m.

ηeis the solar collector efficiency, which can be expressed by

(9)

whereCiis the ratio ofi-th working condition (in the actual solar collector field, there are basically 4 types of heat collectors, which are vacuum, air, hydrogen and light pipe, namelyn=4) of solar collector accounts for the total collector[9];Siis the proportion of all the solar collectors that work normally ini-th condition;ηiis the thermal efficiency of the solar collector under thei-th operating condition.

In Eq.(1),fois the impact factor of solar collector operation and solar tracking, which can be generally considered asfo=0.99.

After the collection of solar energy by the collector, the heat conducting medium passes through the steam generating system to produce high temperature and high pressure steam, and the steam enters the turbine to generate electricity. The actual power generation of the system can be expressed as

Pacture=(Qu-Qloss)ηpower,

(10)

whereQlossis the heat loss in collector field, which can be expressed by[10]

Qloss=csΔTf,

(11)

wherec=0.058 3 W/m2K, ΔTfis the difference between average operating temperature and ambient temperature of solar collector,ηpoweris the efficiency of turbo generator set.

When the solar thermal power plant reaches a certain scale, the relationship between the power generation and the plant area presents a nonlinear relationship because of scale effect, and the capacity of solar thermal power generation system is difficult to calculate directly. After querying the related parameters of several solar thermal power plants that have been built, it is found that due to the existence of capacity scale effect, when the system increases the unit capacity, the required increase in the mirror area is relatively reduced[11]. In order to estimate the capacity of the solar thermal power generation system more accurately, the nonlinear fitting method is adopted in this paper, the fitting curve is shown in Fig.1. When DNI is about 900 W/m2, by comparing the second-order function and the three-order function, the MATLAB is used to fit the parameters, set

P=(As2+Bs+C)Pacture,

(12)

whereA,B,Care fitting coefficients, which can be obtained by fitting;sis solar collector area. Finally, the relationship between solar thermal power plant capacity and plant area is obtained. After verification, the deviation of second-order functions is less than 0.05, which proves that the fitting is basically accurate.

Fig.1 Fitting curve of mirror field area and capacity of power plant

1.2 Generation cost modeling of solar thermal power generation system

At present, there is lack of cost analysis for linear Fresnel solar thermal power station in China. Because the electricity price of linear Fresnel solar thermal power generation relates to the construction cost, operation and maintenance cost, annual power generation, financial cost, tax and so on[12-14], LCOE is used to measure and predict its generation price[15]. LCOE is the international standard for evaluating the unit cost of electricity, which is the total cost of life cycle divided by the total power generated in the life cycle. In general, LCOE can be simplified as

(13)

whereEtotalis the total system power generation, kW/h, which can be expressed by

(14)

whereEtis system annual power generation in yeart,Et=8 760PXfunction,Xfunctionis average power generation ratio;ris capital discount rate;nis operation cycle.

Eq.(15) represents the total cost of the systemCtotal, and the construction cost of the systemItis expressed in Eq.(16).

Ctotal=It+If,

(15)

It=Ccol+Cpow+Cstor+Cother,

(16)

whereIfis the operation cost;Ccol,Cpow,Cstor,Cotherare heat collection system cost, power generation system cost, heat storage system cost and fringe cost respectively, which are expressed in Eqs.(17)-(19).

Ccol=ecols,

(17)

Cpow=eelePNs,

(18)

Cstor=estorPstor,

(19)

whereecolis the unit area cost of solar collector, yuan;sis the collector system area, m2;eeleis the cost of power generation per unit, yuan;Pis the capacity of power plant, kW/h;Nsis the solar multiple, studies have shown that when solar multiple is between 2-2.5, the system generation cost is the lowest[16];estoris the heat storage system cost per unit, yuan;Pstoris the capacity of the heat storage system, kW, in this paper,Pstoris a fitting function, which can be expressed by

(20)

(21)

whereMtis the operating costs of the system in the yeart, yuan, the operation and maintenance cost of solar thermal power plantMtis low, it can be referred to the operation and maintenance costs of the solar energy generating systems (SEGS) power plant in California, USA, which is about 0.04 dollars per kWh;ris capital discount rate;nis the operation cycle;Cotheris fringe cost, which accounts for 10% of the total cost of the system.

2 Analysis and comparison of optimization algorithms

2.1 NSGA-II algorithm

Non-dominated sorting genetic algorithm (NSGA) is widely used in various optimization problems, but NSGA lacks a strategy for protecting elite individuals. NSGA-II has improved NSGA in three main areas: (1) Fast non-dominated sorting algorithm is proposed, which reduces the computational complexity and can combine parent population and the progeny population, the next generation population can be selected from the combined space, so as to retain all the best individuals; (2) The elitist strategy is introduced to ensure that no good individuals are lost during the evolution process, thus improving the reliability of the optimization results; (3) In the algorithm, the crowding and crowding comparison operators are used to distribute the evolutionary individuals evenly to the whole Pareto domain, thus ensuring the diversity of the population[17]. NSGA-II uses an analog binary crossover to restructure the genome, the mode of individual production is

(22)

The specific steps of NSGA-II are as follows:

Step 1: generate the initial populationPand the null outer non-inferior solution setNP;

Step 2: copy the non-inferiority individuals in the populationPto the non-inferior solution setNP;

Step 3: eliminate the solutions in the setNPthat subject to individual dominance in populationP;

Step 4: if the number of non-inferior solutions retained in the setNPexceeds the maximum given previously, then the clusterNPis modified by clustering analysis to eliminate the superfluous solution;

Step 5: calculate the fitness values of each individual in the populationPand the setNP;

Step 6: use the binary tournament method to select individuals from the (P+NP) into the next generation;

Step 7: perform crossover and mutation operations on individuals;

Step 8: if the maximum algebra is reached, stop searching; otherwise go to step 2.

2.2 Algorithm test

In Ref.[18], NSGA-II algorithm and particle swarm algorithm are compared; generational distance (GD) is used as an evaluation index of astringency; spacing (SP), a spatial evaluation method proposed by Schott, is used as an evaluating indicator of distribution. The definition of GD is as follows

(23)

wherenis the number of solutions in a solution set;diis the least Euclidean distance between each solution and the known Pareto front. The smaller thedGDis, the better the convergence of the algorithm is.

The definition ofdSPis

(24)

To illustrate the applicability of NSGA-II in solar thermal power generation, the optimization results of NSGA-II are compared with the results of particle swarm optimization (PSO). Set the population number and the maximum number of iterations as 200, use NSGA-II algorithm and PSO algorithm to optimize the objective function respectively, and the result is shown in Fig.2.

Fig.2 Optimization results of LCOE

By calculation,dGDNSGA-II=2.591e-4,dGDPSO=1.025e-3,dSPNSGA-II=7.981e-3,dSPPSO=3.513e-2, which shows that the NSGA-II algorithm is superior to PSO algorithm both in convergence and distribution.

According to Fig.2, the results of NSGA-II algorithm are consistent with the results of PSO, and the curve under NSGA-II is smoother, the distribution is also better than the PSO algorithm, which can be used to optimize the electricity cost and capacity of solar thermal power generation.

3 Simulation and analysis

3.1 Impact of loan situation on LCOE

[(1+7.9%/12)360-1]}×360+It×0.3.

(25)

By introducing Eq.(25) into Eq.(2), the LCOE of the solar thermal power generation under the condition of the existence of the loan can be obtained. While the collector area is 20 000-1 100 000 m2, the heat storage duration is 6-11 h, the thermal storage quality is heat conducting oil, the solar multiple is 2, and the capital discount rate is 8% per year. Here, the relationship between LCOE and capacity of the linear Fresnel solar thermal power generation system is shown in Fig.3.

Fig.3 LCOE with or without loans

From Fig.3, it can seen that the existence of loans has a great impact on the LCOE of solar thermal power generation. When the capacity of power station is around 50 MW, solar thermal power generation systems with 70% loans cost more than 34% of electricity without a loan. To reduce the cost of solar thermal power stations, the state must provide loans with low interest rates or other preferential policies. Table 1 shows the impact of loan conditions on LCOE by using NSGA-II algorithm and PSO algorithm respectively. Both two algorithms have the consistent impact of loan policy on LCOE.

Table 1 Impact of loan conditions on LCOE (a) NSGA-II algorithm

(b) PSO algorithm

3.2 Impact of power plant capacity on LCOE

In the case of loans, the mirror area is 20 000-7 500 000 m2, the heat storage duration is 6-11 h, the thermal storage quality is heat conducting oil, the solar multiple is 2, and the capital discount rate is 8% per year. Here, the relationship between LCOE and capacity of the linear Fresnel solar thermal power generation system is shown in Fig.4.

Fig.4 Capacity and LCOE of solar thermal power generation system

The data analysis is shown in Table 2, under the same conditions, the optimization results of the two algorithms both show that due to the scale effect of the solar thermal power plant, the greater the capacity of the power plant, the lower the LCOE. When the capacity of power station is around 50 MW, LCOE dropped to less than 1.15 yuan.

Table 2 Relation between system capacity and LCOE (a) NSGA-II algorithm

(b) PSO algorithm

3.3 Impact of different thermal storage properties on LCOE

In the case of loans, the mirror area is 20 000-5 000 000 m2, the heat storage duration is 6-11 h, the thermal storage fluids are heat conducting oil and molten salt respectively, the solar multiple is 2, and the capital discount rate is 8% per year.

Fig.5 Effect of thermal storage on LCOE

Here, the relationship between LCOE and capacity of the linear Fresnel solar thermal power generation system is shown in Fig.5.

Table 3 presents the partial data analysis of the influence of different thermal storage properties on LCOE in PSO algorithm and NSGA-II algorithm.

Table 3 Effects of different thermal storage properties on LOCE (a) NSGA-II algorithm

(b) PSO algorithm

According to the result, when the solar thermal power plant is large enough, the molten salt storage system can significantly reduce the LCOE level.

4 Conclusion

In this paper, NSGA-II algorithm and PSO algorithm are used to optimize the LCOE level of linear Fresnel solar thermal generating station under different conditions, conclusions can be draw as follows: (1) Due to the scale effect of solar thermal power generation system, the larger the scale is, the lower the LCOE is; (2) In the presence of loans, the LOCE of solar thermal power generation system will be significantly improved, the capacity will be higher than the current online guidance price of 1.15 yuan/kWh; (3) When the scale of solar thermal power generation system is large enough, the use of molten salt heat storage material can significantly reduce the LCOE of the system.

Solar thermal power generation project practice and large-scale production have just started in our country, in addition to technological innovation, the state should also provide more preferential policies, such as preferential loans, land cost reduction, research support, price compensation, etc., so as to promote its faster development.

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