Optimal design of a solar-hybrid cogeneration cycle using Cuckoo Search algorithm

Applied Thermal Engineering 102 (2016) 1300–1313

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Optimal design of a solar-hybrid cogeneration cycle using Cuckoo Search algorithm M.H. Khoshgoftar Manesh ⇑, M. Ameryan Energy & Water Conservation Research Lab, Division of Thermal Sciences & Energy Systems, Department of Mechanical Engineering, Faculty of Technology & Engineering, University of Qom, Qom, Iran

h i g h l i g h t s
Effective time-saving procedure.
Using simple parallel computing exergoeconomic optimization.
Optimum design of solar-hybrid cogeneration cycle based on the Cuckoo Search.
Appears effective in optimizing thermodynamic cycles.

a r t i c l e

i n f o

Article history: Received 4 November 2014 Accepted 30 March 2016 Available online 12 April 2016 Keywords: Cuckoo Search Levy flight Renewable energy Solar energy Optimization Cogeneration CGAM problem Solar hybrid cogeneration CO2 Cost

a b s t r a c t In this paper optimum design of solar-hybrid cogeneration cycle based on the Cuckoo Search (CS) algorithm is presented. The CS is one of the recently developed population based algorithms inspired by the behavior of some cuckoo species together via the Levy flight behavior of some birds and fruit flies. Moreover, solar power tower technology is practical for utilization in conventional fossil fired power cycles, in part because it can achieve temperatures as high as 1000 °C. An exergoeconomic optimization is reported here of a solar-hybrid cogeneration cycle. Modifications are applied to the well-known the prescribed simple cogeneration (CGAM) problem through hybridization by appropriate heliostat field design around the power tower to meet the plant’s annual demand. The hybrid cycle is optimized utilizing a CS and compared with the results of the Genetic Algorithm (GA) in Matlab toolbox. Considering exergy efficiency and product cost as objective functions, and principal variables as decision variables, the optimum point is determined. The corresponding optimum decision variables are set as inputs of the system and the technical results are a 48% reduction in fuel consumption which leads to a corresponding decrease in CO2 emissions and a considerable decrease in chemical exergy destruction as the main source of irreversibility. In the analyses, the net power generated is fixed at 30 MW with a marginal deviation in order to compare the results with the conventional cycle. Despite the technical advantages of this scheme, the total product cost rises significantly (by about 87%), which is an expected economic outcome. Effective time-saving procedure using simple parallel computing, as well as utilizing reliable analysis and design tool are also some main features of the present study. The results show that the proposed method appears effective in optimizing thermodynamic cycles. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Solar thermal power plants can contribute to this aim, however, and can help provide energy-supply security, especially when integrated with thermal energy storages and/or used in solar–fossil

⇑ Corresponding author. E-mail addresses: [email protected], (M.H. Khoshgoftar Manesh). http://dx.doi.org/10.1016/j.applthermaleng.2016.03.156 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

[email protected]

hybrid operation strategies. Therefore, many predict that solar thermal power plants will achieve a significant market share of the energy sector in the future [1]. Solar energy is an intermittent energy source. Current solar power plants that are operated with a solar-only operation strategy and use thermal energy storages to extend the operation to hours when the sun does not shine usually cannot entirely provide power on demand while at the same time achieving economic viability. Therefore such solar power plants are generally unable to

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Nomenclature LHV CP e h _ m P T _ W Z

lower heating value specific heat at constant pressure specific exergy specific enthalpy mass flow rate pressure temperature power cost associated with a component

Greek letters eap air pre-heater effectiveness gsc compressor isentropic efficiency

gst ghrsg

gas turbine isentropic efficiency HRSG first law efficiency

Subscripts air stream of air ap air preheater sc compressor st turbine fuel fuel gas stream of combustion gases steam flow of feed water/steam total total plant

satisfy base-load electricity needs, necessitating utilities using solar energy to provide backup power, usually from conventional fossil fired power plants. This challenge can be in part overcome by the use of additional fossil fuel to generate the heat in a solarhybrid power plant [1]. Although solar radiation is a high quality energy source, due to its high potential temperature and exergy, its source, its power density at the earth’s surface makes it difficult to extract work and achieve reasonably useful temperatures in common working fluids [2]. Therefore, solar-hybrid thermal power plants usually employ optical concentration. A practical example is solar power tower technology, which can harness the available solar irradiation with concentration ratios up to 1000 suns to achieve high receiver temperatures [3]. High-temperature solar power tower technology is utilized in solar gas turbine systems to heat the pressurized air in a gas turbine before it enters the combustion chamber (Fig. 1a). Also, the CGAM Problem has been shown in Fig. 1b. The solar heat can therefore be utilized via recuperation in a combined gas turbine cycle. The combustion chamber provides heat to raise the temperature from the receiver outlet temperature (800–1000 °C at the design point) to the turbine inlet temperature (950–1300 °C); it also provides a constant turbine inlet conditions even though the solar input fluctuates. Current solar power designs are limited by conventional fluid receivers [4]. Two experimental feasibility investigations of a hybrid Brayton cycle have been reported:
Solar hybrid gas turbine electric power system (SOLGATE) [3]: the SOLGATE project involved the design and fabricate a 250 kW gas turbine with three solar receivers. Solar hybrid operation was successfully demonstrated in 2005 with kerosene as a backup fuel. A pressurized volumetric air receiver with a secondary concentrator (REFOS receiver technology) was developed and successfully tested as part of the study, as one of several German R&D projects [5]. The REFOS type receivers [6] utilized for SOLGATE performed well. An air exit temperature of 960 °C was achieved in first cycle. The previous receiver setup could be modified to attain 1030 °C in the second cycle of project.
Solar-hybrid power and cogeneration plants [7]: the SOLHYCO project successfully developed and tested an efficient, reliable and economic solar-hybrid cogeneration system based on a 100 kW micro turbine. The system can operate in parallel with varying input contributions from solar energy and fuel [7]. In this paper, the well-known CGAM problem [8], which is based on a fossil fuel fired cogeneration cycle, is used as a case study to allow hybridization to be investigated in terms of thermodynamics,

Fig. 1. (a) Hybrid cogeneration cycle [21]. (b) Flow diagram for the CGAM cogeneration plant.

annual solar share, and economics. The solar field is designed to permit harnessing of the maximum available annual solar irradiation. A hypothetical site is considered with conditions typical of

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the Mojave Desert in California where different power tower fields have been implemented. So as to operate and optimize the hybrid cycle under different conditions, a code is developed in MATLAB to evaluate the overall behavior of cycle determined while allowing varying performance conditions to be defined. The economic analysis is based on the method proposed elsewhere [9,10] which estimates levelized costs of products and by-products based on varying economic parameters for a plant with a 20-year commercial life. In this regard, powerful optimization methods inspired by cuckoo bird behaviors have been introduced. Cuckoo bird lays their eggs in neighbor nests of other species of birds to be incubated and raised. A cuckoo egg mimics host eggs convincingly. There is a probability that the host bird notices the cuckoo’s egg and kills it or abandons its nest. Consequently, the cuckoo egg gets rotten. Limit number of cuckoo birds can leave in an area. Exceeding it, weaker ones died for reasons such as inadequate food. Yang and Deb present Cuckoo Search algorithm (CS) inspired by brood parasitism behavior of cuckoos. Then summarize the CS algorithm in

terms of what it actually does to the parameter sets [11] as shown in Fig. 2. In the field of thermoeconomics [12–17], design optimization of energy systems, which aims at minimizing the total levelized costs of products, generally competes with thermodynamic performance. Thermoeconomic analyses of thermal systems are often focused on the economic objective. However, knowledge of only the economic minimum may not be adequate for proper decision making, since solutions with a higher thermodynamic efficiency, in spite of small increases in total costs, may result in more advantageous designs [18]. Therefore, multi-objective optimization [19–32] is often useful. For instance, optimization of a system using genetic algorithm (Such as that provided by MATLAB Optimization toolbox) and CS algorithm, with exergy efficiency and final product cost as objective functions, allows optimal workable designs to be found that simultaneously satisfy thermodynamic and economic objectives. Finding the optimum design point through the use of Pareto Frontiers, allows overall results to be developed that focus on various factors.

Fig. 2. Algorithm of Cuckoo Search [11].

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2. System overview 2.1. The CGAM problem In 1990, a group of concerned energy experts in the field (C. Frangopoulos, G. Tsatsaronis, A. Valero, and M. von Spakovsky) decided to compare their methodologies by solving a predefined and simple optimization problem named the CGAM problem, after the first initials of the participating investigators. The models used in the CGAM problem are realistic but incomplete from an engineering viewpoint [8]. Using thermo-economic optimization a realistic and complete system is obtained. The CGAM problem considers a cogeneration plant, which has the structure shown in Fig. 1b and delivers 30 MW of electricity and 14 kg/s of steam at 20 bar. The cogeneration plant consists of a gas turbine followed by an air preheater that uses part of the thermal energy of the turbine exit gases, and a heat-recovery steam generator (HRSG) in which the required steam is produced. Fig. 3 temperature profiles for the preheater and HRSG, respectively (see Fig. 4). 2.1.1. Thermodynamic model A simplified model is provided to solve the physical model and to calculate the state variables for the cogeneration plant, based on the following assumptions:
The cogeneration system operates at steady state.
Ideal-gas mixture principles apply for the air and the combustion products.
The fuel (natural gas) is taken as methane modeled as an ideal gas, and is provided to the combustion chamber at the required pressure by throttling from a high pressure source.
The combustion in the combustion chamber is complete, and N2 is treated as inert.
The heat transfer loss from the combustion chamber is 2% of the fuel lower heating value, and all other components operate without heat losses. In thermal systems design and optimization, it is convenient to identify two types of independent variables: decision variables and parameters [8]. The decision variables may be varied in optimization studies, but the parameters remain fixed in a given application. All other variables are dependent variables and their values are calculated from the independent variables using the thermodynamic model. 3. Hybridized cogeneration plant The conventional cogeneration plant described earlier is modified in order to evaluate the performance when a solar contribution is added to the cycle by a solar receiver on top of a tower that absorbs the concentrated solar irradiance from a surrounding field.

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The receiver is located after the air preheater and reheats the compressed air entering the combustion chamber (Fig. 1a). In order to simplify the analysis, only one receiver is assumed to operate in the cycle while in reality [3,7] for a pressurized volumetric receiver model the maximum size is limited mainly by the quartz window [3]. Therefore, the receiver in a large power plant consists of a cluster of single receiver modules with secondary concentrators based on the demand of the plant which is related to working fluid mass flow rate and technological capability. Also, other connecting parts like piping systems are merely considered in the economic portion of this study. Thus, only the effect of preheating by consideration of solar irradiance condition is analyzed. In this article, therefore, it is assumed that the receiver is a single module and the temperature rise occurs in one step. The physical and thermodynamic models of the new modified plant do not differ from the original CGAM one, except that, a new component (Solar Receiver) is included. In the receiver energy balance, the absorbed solar overall heat rate is an external energy source (Fig. 5), thereby linking, and the solar field to the conventional cycle. The governing physical model equations for the solar receiver are as follows:

_ a h3 þ Q_ s;absorbed ¼ m _ a h30 m Q_ s;absorbed ¼ DNI  Amirror  gfield  greceiv er

gfield ¼ gatmospheric  greflection  gCos  gshading  gblocking  gAttenuation  gIntercept p30 ¼ p3 ð1  Dpreceiv er Þ The solar field design section presents the applied method to derive one overall equation for collected solar energy and other design details. 3.1. Solar field design The design of the solar field and its overall efficiency are affected by several factors: atmospheric conditions and reflectivity, blocking and shading, cosine effects, attenuation, and intercept. These are often assessed in terms of efficiencies. In this study, we presume low land costs because the system is assumed to be located in the Mojave Desert. Consequently, mirrors are taken to be installed at appropriate distances with respects to each other to avoid shading and blocking effects (Fig. 6), so these effects are neglected here. Based on heliostat manufacturer data the reflection efficiency is constant. The reflection efficiency is assumed constant, ignoring mirror degradation and soiling. Yet, atmospheric conditions and cosine efficiencies have time dependent behaviors which have to be determined by transient functions in order to obtain precise results. Here, therefore, corresponding MATLAB codes are developed with appropriate time

Fig. 3. Temperature profiles through the air preheater and the HRSG.

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Fig. 4. Honeycomb arrangement of receiver modules [3].

Table 1 Details for the solar field design.

Collected Solar Energy

Location of field

Heliostat area Receiver cluster area

T3

T3' Fig. 5. Solar receiver control volume.

steps to calculate the transient value of available solar power at the edge of the receiver cluster. Due to the application of the Total Revenue Requirement (TRR) economic method, which considers annual behavior to calculate the levelized cost of products, the transient behavior of the solar field must be considered in annual average data. In order to accelerate the optimization process, the overall result for the solar field is entered into the main optimization codes by a unit derived equation which requires only number of mirrors to calculate the solar power at the edge of receiver. By running the solar codes in an appropriate interval of mirror numbers [6000–9000], a large set of data results. The solar power to the receiver was calculated for 6000–9000 heliostats and was curve fit as follows:

Q s;field ¼ 6:499  n mirror þ 3823 Details for the solar field design are presented in Table 1. The method applied for field design is described in Appendix D. The designed solar field layout is depicted in Fig. 7. Moreover, as

Total field area Number of mirrors Tower height

gCosine gReflectiv ity gAtmospheric gBlocking gShading gIntercept gAttenuation gReceiv er

Dagget, Mojave, California, US

Long. 116.88° Lat. 34.86° Alt. 700 m 16 m2 with 4 m  4 m square dimensions 2 120 m (estimated overall area of receivers based on [8]) 1700 m  800 m 8800 (obtained through optimization) 150 m 0.82 (calculated annual average dynamic value) 0.90 0.59 (calculated annual average dynamic value) 1 1 0.85 0.92 0.56 (according to [4])

shown in Fig. 1a. the mirrors are directed toward south depending on the field location. 3.2. Exergy analysis Exergy analysis aims at the quantitative evaluation of meaningful efficiencies and the exergy destruction rate (E_ D ) and losses associated with a system [9]. We consider each component as a control volume for exergy analysis. A general exergy balance can be written as:

  X   X dEcv X T0 _ _ cv  p dV cv þ 1 Ei þ Ee  E_ D ¼ Qj  W 0 dt Tj dt e j i

Fig. 6. Depiction of shading and blocking effects.

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Fig. 7. Solar field layout.

At steady state, dEcv =dt ¼ 0 and dV cv =dt ¼ 0. An exergy efficiency can be calculated as the percentage of the exergy supplied to the system that is associated with the product (s) of the system. The product of a cogeneration system can be defined as the sum of the net electrical power generated and the net increase of the exergy rate of the feed water. Then,

_ W_ þ ðE_  E_8 Þ W ¼ net P 9 _Ei Here, E_ i denotes the total inlet exergy rate to the system by air stream, fuel and solar irradiation in Hybrid Case. Accordingly, exergy efficiency is calculated for the hybrid cycle based on two viewpoints. One considers solar power as an input source of energy and the other neglects solar power as an input, essentially due to it being free of charge. The latter efficiency permits comparisons between the main plant components of both cycles. 3.3. Economic model Accurate cost estimation is a key factor in successful design. In order to define a cost function which depends on the optimization parameters of interest, component costs have to be expressed as functions of thermodynamic variables. To optimize important parameters, costs are expressed as functions of thermodynamic variables, especially of the final product(s). In this study, the revenue requirement method [33] is applied to estimate the levelized cost of products for entire operation lifetime of the plant. This calculation involves the following steps [8]:
Estimate the Total Capital Investment (TCI).
Determine the economic, financial, operation, and market input parameters for the detailed cost calculation.
Calculate the total revenue requirement.
Calculate the levelized product cost. The annual total revenue requirement (total product cost) for a system is the revenue that must be collected in a given year through the sales of all products to compensate the operating company for all expenditures incurred in the same year and to ensure sound economic plant operation [33]. The total capital investment (TCI) is broken down into two major categories: fixed capital

investments and other outlays. Details of these are founded on the overall purchased equipment cost (PEC), including those for the solar equipment. The capital investment breakdown is shown in Appendix D. 4. Optimization In this study, a multi-objective optimization scheme is developed and applied for both plants to find solutions that satisfy simultaneously exergetic as well as economic objectives. The optimization process is executed by a particular class of search algorithms known as objective GA and CS algorithm for evaluation. Using a multi-objective approach, the decision maker is able to choose from solutions having the lowest costs at higher efficiencies. This takes into account how higher technology plants often save more fuel than those with minimum costs or, alternatively, how plants can achieve minimum expenditures at a given efficiency. This necessitates a search for the population of Pareto optimal solutions with respect to the two competing objectives; it is not possible to find a single solution that optimizes both targets. Rather, it is necessary to find the set of optimal solutions that lead to the highest efficiencies at fixed costs, or the lowest costs at fixed efficiencies. In general, the design process involves multiple objectives: thermodynamic (e.g. maximum efficiency or minimum fuel consumption), economic (e.g. minimum cost per unit of time and maximum profit per unit of production) and others [18]. The two objective functions of the multi-criterion optimization problem considered here are the exergy efficiency of the cogeneration plant (to be maximized) and the total cost rate of operation (to be minimized). The mathematical formulation of the two objectives is as follows:

exergetic n ¼

_ net þ m _ steam ðe9  e8 Þ W _ fuelefuel m

_ economic C total ¼ C_ steam þ C_ electricity The decision variables are varied during the optimization. The thermodynamic and economic models of the CGAM problem present five degrees of freedom. In order to speed up the optimization and define the search space for the optimization procedure, a variation range is specified for each decision variable as follows:

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c ¼ 0:01  s  ðhp  hb Þ

r_c (compressor pressure ratio): 9 6 r_c 6 12. gsc (compressor isentropic efficiency): 0.82 6 gsc 6 0.90. T4 (gas turbine inlet temperature): 1450 6 T4 6 1650. gst (gas turbine isentropic efficiency): 0.84 6 gst 6 0.90. eap (air pre-heater effectiveness): 0.50 6 eap 6 0.85.

The value 0.01 is typical length scale. 0 hp

The variable eap is used instead of T3 (used in the original CGAM problem) to reduce the number of non-feasible solutions that occur during the optimization process. For the hybrid cycle, the following decision variables are considered additionally:
Nmirror (numbers of heliostat mirrors): 7500 6 Nmirror 6 10,000.
T30 (solar heating temperature): 1200 6 T30 6 1300.

In this paper, the CS algorithm is used for optimization of CGAM problem. In CS three rules are followed: I. In each iteration, each individual cuckoo bird produces just one egg and leaves it at a random host nest. II. The best quality eggs survive and exist in next generation. III. The number of host nest is predefined and eggs recognized and killed by host with a probability pa 2 [0, 1]. To make this rule less complex, the fraction pa of n nest exchange with new random solutions. To utilize CS in maximization problem, the fitness value of a solution can be proportional to the fitness function value. For other type of problem, fitness function likes used in other population based methods may be used such as genetic algorithm and particle swarm optimization. In this algorithm, iteratively solutions are replaced with new better solutions. An egg in a nest is a solution, and a cuckoo bird is new solution. Initial cuckoo population sized P, are produced randomly. ‘‘The fitness value – proportional to the fitness function value” is awkward, and poorly structured after the use of evolutionary language associated with the (very slow) ‘‘genetic” algorithm. Why ‘‘proportional”? Clarify if you are normalizing or using a proportionality factor.

hp ¼ R  rand þ V min

ð1Þ

Here, p’th cuckoo or egg is denoted by hp ; 1 6 p 6 P. Vmin and R are minimum and range of input space. And rand is n-dimensional array, including numbers between 0 and 1. Lévy flight is a random walk which has characteristic of an instant jump sequence selected from power-law distribution function with a heavy tail. With CS, a Lévy flight is calculated by Mantegna’s algorithm for both local and global searches. First, the step length is computed as: 1=v

S ¼ ½s1 ; . . . ; sn  ¼ U 1 =ðabsðU 2 ÞÞ

ð2Þ

U 1 and U 2 are n-dimensional array uniformly distributed in [0, r] and [0, 1] respectively. r is computed as follows:

Cð1 þ vÞ sinðpvÞ Cðð1 þ vÞ=2Þv2ð1vÞ=2

!

ð3Þ

where is v a constant number between 1 and 2. Here, v is taken 1.5 as it generally is assumed in many studies. The gamma function is defined as follows:

Z

CðeÞ ¼

1

ec me1 dm

¼ hp þ c  Rn

ð6Þ

where Rn is a n-dimensional array of random numbers in range in 0 0 to 1, and hp is the next solution. 4.2. Physical constraint Heat exchange between hot and cold streams in the air preheater and in the HRSG, must satisfy the following feasibility constraints:
Air preheater: T5 > T3; T6 > T.2
HRSG: DTP = T7P–T9 > 0; T6 P T9 + DTP;T7 P T8 + DTP; ghrsg 6 1

4.1. Cuckoo Search algorithm

r¼

ð5Þ

ð4Þ

0

Second the maximum step size, c, is computed considering keeping the current best answer denoted by hb :

An additional constraint, with respect to the original CGAM problem, is imposed on the exhaust gas temperature, which must not fall below 380 K. For the conventional cycle, the net target power is fixed at 30 MW. Yet in the hybrid mode, due to solar irradiance fluctuations and to obtain more feasible design points, the net power is assumed to have a 400 kW deviation relative to the annual base design. Additionally, in the primary steps of plant design, no adequate design point group was extracted for a fixed 30 MW power for the hybrid mode, which could allow further steps for optimization. The other defined constraint is fuel flow rate, which always has to be less than that for the corresponding conventional mode (as a final goal). This constraint is imposed when more fuel consumption rate (compared to conventional mode) is witnessed in hybrid mode in early hours of sun rise and symmetrically latter hours of sun set. The reason is determined to be the ratio of preheat temperature to excess air intake; by decreasing the fuel consumption in hybrid mode in order to maintain the electricity generation at 30 MW, a higher air intake is required and this additional air needs to be preheated to an adequate level in the hours stated. But this condition could not be met. So, by omitting those hours in performance schedule, our defined constraint is satisfied. The two new constraints are as follows: ‘‘The other defined constraint is fuel flow rate, which always has to always be less than that for the corresponding conventional mode (as a final goal). This constraint is imposed when more fuel consumption rate (compared to conventional mode) is witnessed in hybrid mode in early hours of sun rise and symmetrically in latter hours of sun set. ...But this condition could not be met. So, by omitting those hours in performance schedule, our defined constraint is satisfied”.

_ net < 30; 400 29; 600 < W _ _ fuelconv entional mfuelhybrid < m 4.3. Optimization runs 4.3.1. Conventional case Primarily, the conventional CGAM cycle is optimized to determine the base case study for comparison with hybridization cases using GA and CS algorithms. Fig. 8 presents the Pareto optimum solutions for the CGAM cycle for the objective functions indicated using GA algorithm. As shown in this figure, although the total exergy efficiency of the plant is increased t 52.4% to, the total cost rate of products increases very slightly. Increasing the total exergy efficiency from 52.4 to 52.7% corresponds to moderate increase in the cost rate of products. Further increases in the exergy efficiency from 52.7% to higher values lead to a significant increase of the total cost rate. In multi-objective optimization, a process of

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Total Cost Rate of Product ($/h)

30000 25000 20000

EP

15000 10000 5000 51.4

51.6

51.8

52

52.2

52.4

52.6

52.8

53

53.2

53.4

Total Exergetic Efficiency (%) Fig. 8. Pareto frontier, showing best trade-off values for the objective functions (for conventional case).

Total Cost Rate of Product ($/h)

decision-making for selection of the final optimal solution from the available solutions is required. The process of decision-making is usually performed with the aid of a hypothetical point in Fig. 8, named as Equilibrium Point (EP), for which both objectives have their optimal values independent of the other objective. It is clear that it is impossible to have both objectives at their optimum point simultaneously and, as shown in Fig. 8, the equilibrium point is not a solution located on the Pareto frontier. The closest point of the Pareto frontier to the equilibrium point might be considered as a desirable final solution. In selection of the final optimum point, it is desired to attain a better value for each objective than its initial value from the base case problem. On the other hand, the stability of the selected point when one of objective varies is highly important. Therefore, a part of Pareto frontier is selected in Fig. 9 for decision-making, coinciding with the domain between the horizontal and vertical lines. A final optimum solution is selected with an exergy efficiency of 52.73% and a total product cost rate of 10851.47 $/h (see Fig. 9). Note that the selection of an optimum solution depends on the preferences and criteria of each decision maker. Therefore, each decision maker may select a different point as an optimum solution to better suit his/her desires. The related values of the decision variables and the two objective functions, including the total product cost and the total exergy efficiency, are listed in Table 2.

4.3.2. Hybrid case According to the multi-objective optimization study carried out by Toffolo and Lazzaretto in [18], it becomes clear that the last point of the cycle that is exiting part of HRSG, more important in optimization process. Therefore, the mentioned authors divide their work into two sections: Free exhaust temperature and Constrained exhaust temperature as we do so here in Hybrid Case optimization while in Conventional case optimization, no significant change investigated by omitting the exhaust temperature as a constraint. The temperature of the HRSG exit gases plays an important role in verifying the optimum workable design point for the hybrid cycle. It is considered as a final monitor for cycle performance yet, as being the last point in the cycle, it does not have direct thermodynamic effect on any of states. In the first run for the hybrid cycle, no feasible design point is detected using the presented decision variable intervals. This is an inevitable result because, owing to the significant decrease in fuel/air ratio in the hybrid cycle, which is the final design target, the exergy of the gas products entering the HRSG exhibits a sharp decrease (almost half), leading to insufficient exergy to produce the required saturated steam (14 kg/s). But, while neglecting the exhaust temperature constraint, optimization still leads to logical set of design points (Fig. 10). Therefore, it becomes clear that the overall plant performs well (see Fig. 11).

19000 17000 15000 13000 11000 9000 52.6

52.73981866, 10851.47376 52.65

52.7

52.75

52.8

52.85

Total Exergetic Efficiency (%) Fig. 9. The optimum point details.

52.9

52.95

53

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Table 2 Comparison of optimum values in conventional and hybrid plant cases. Conventional (GA)

Hybrid (GA)

Conventional (CS)

Hybrid (CS)

Nmirror (kg/s) T4 (K) gsc (%) gst (%) r_c

– 0.521 – – 1590 0.8602 0.9087 10.6184

1207.09 0.889 8800 9.69 1582.08 0.8632 0.9193 9.55

– 0.53 – – 1591.2 0.8612 0.9091 10.6214

1208.25 0.89 8800 9.69 1583.11 0.8644 0.9196 9.56

Dependent variables T3 (K) T2 (K) (kg/s) (kg/s) (kW) T7 (K)

818.53 611.01 74.50 1.5663 30,000 436.5533

962.67 594.90 80.25 0.82 30,060 385.13

819.24 611.24 74.52 1.5663 30,000 436.5821

962.94 595.12 80.29 0.82 30,060 385.79

Exergy destruction rate AC (MW) APH (MW) Solar (MW) CC (MW) GT (MW) HRSG (MW)

2.4827 0.0184 – 23.92 1.52 9.94

1.79 1.71 34.78 11.64 1.44 2.6

2.4827 0.0184 – 23.92 1.52 9.94

1.79 1.71 34.78 11.64 1.44 2.6

Exergy rate for significant streams 30 (MW) 4 (MW) (MW) 7(loss) (MW)

– 90.06 23.13 0.4247

59.8 91.1 12.47 1.03

– 90.06 23.13 0.4247

59.8 91.1 12.47 1.03

Objectives Total cost rate of product ($/h) Total exergy efficiency (%)

10851.47 52.74

20296.98 41.6

10852.81 52.77

20299.01 41.83

Other results Total input exergy rate (MW) Total exergy destruction rate (MW) Average solar share in hybrid mode (%) Annual average solar share (%) (considering night hours) Specific cost of elec. ($/kW h) Specific investment for CO2 reduction ($/kgCO2) CO2 emission rate (ton/year)

81.08 37.89 – – 0.06526 – 114,375

94 53.98 35 14 0.08533 2.13 86,115

81.08 37.89 – – 0.06528 – 114,375

94 53.98 35 14 0.08536 2.13 86,115

Decision variables T30 (K)

eap

Accordingly, two changes are made: decreasing the air preheater effectiveness (eap) interval to 0.30, and increasing the combustion temperature (T4). Note that the allowed temperature for combustion with regard to technological limitations for the first stage of turbine blades is 1650 K [18] yet, in this case, in order to find a possible design availability we let T4 increase to 1750 K. Eventually, an expected illogical cost results as the optimum point, which is almost six times greater than its free temperature result in the hybrid mode. On first consideration, this result was felt not to be acceptable because there always must be a design solution and there must be adequate exergy to produce 14 kg/s of steam in the hybrid mode. Through hybridization, the constrained target is the same net power, but the new method consumes less fuel, so a question arises of how the exergy flowing into the gas turbine could be held fixed. The answer is having more air intake in the hybrid mode compared to the conventional CGAM mode. Correspondingly, in the air preheater more energy is needed to warm the compressed air, so the inlet stream has less energy compared to the conventional mode. By decreasing the effectiveness of this equipment and increasing the injection of fuel into combustion chamber, the 14 kg/s steam generation can still be met, yet. But this approach can lead to an unreasonable cost rate. As a solution, the steam mass flow rate is considered as another decision variable, allowing the genetic algorithm to find a logical design point itself with respect to the other seven variables. The allowable range is as follows:


m8 (injected water in HRSG): 5 6 m8 6 15. Fig. 12 presents the Pareto optimum solutions for the hybrid system. Although the total exergy efficiency of the plant increases to 41.3%, the total cost rate of products increases slightly. Increasing the total exergy efficiency from 41.3% to 41.6% corresponds to the moderate increase in the cost rate of product. Further increasing the exergy efficiency from 41.6% causes a significant increase of the total cost rate. The process for selection of the final optimal solution from the available solutions is the same as for conventional cycle. As a result, a final optimum solution is selected with an exergy efficiency of 41.6% and a total cost rate of product of $20296.9/h, as indicated in Fig. 13. The related values of decision variables and two objective functions, including the total cost of product and the total exergy efficiency, are listed in Table 1. 5. Results and discussion Table 2 presents and compares the cycle properties of both plants according to corresponding optimum points using CS and GA algorithms. The resulting optimum decision variables are considered as input parameters in order to determine the cycle behavior. The overall net electrical power generated in the hybrid cycle exhibits a 60 kW deviation from the fixed power for the CGAM problem that is accepted. This is because the sun is a fluctuating energy source; this power could deviate by about 800 kWe due

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Total Cost Rate of Product ($/h)

M.H. Khoshgoftar Manesh, M. Ameryan / Applied Thermal Engineering 102 (2016) 1300–1313

32000 30000 28000 26000 24000 22000 20000

45

45.3

45.6

45.9

46.2

46.5

46.8

47.1

47.4

47.7

Total Exergetic Efficiency (%)

Total Cost Rate of Product ($/h)

Fig. 10. Pareto frontier (for Conventional Case – CS).

330000 280000 230000 180000 130000 80000 40.6

40.7

40.8

40.9

41

41.1

Total Exergetic Efficiency (%) Fig. 11. Pareto frontier (for Hybrid Case – CS).

Total Cost Rate of Product ($/h)

20800 20700 20600 20500 20400 20300 20200 20100 40.9

41

41.1

41.2

41.3

41.4

41.5

41.6

41.7

41.8

41.9

Total Exergy Efficiency (%) Fig. 12. Pareto frontier, showing best trade-off values for the objective functions (for Hybrid Case).

to transient effects during sunset and sunrise hours. As anticipated, the fuel consumption rate decreases by 47% in the hybrid mode, which consequently avoids 24.5 tons of CO2 annual emissions. Considering roughly the same net power is delivered with a significant reduction in fuel input, despite all cycle modifications, the gas stream exergy input to the turbine must remain almost constant

for the hybrid plant compared to the conventional one. This requires more air intake and efficient components. Accordingly, the air mass flow rate increases by about 6 kg/s and the efficiency of each component rises marginally. Besides the eight decision variables (is treated as a variable) for the hybrid cycle, the exit exhaust temperature (T7) is a significant

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M.H. Khoshgoftar Manesh, M. Ameryan / Applied Thermal Engineering 102 (2016) 1300–1313

Total Cost Rate of Product ($/h)

20500 20450 20400 20350 20300

41.60225421, 20296.98924

20250 20200 20150 20100 41.5

41.55

41.6

41.65

41.7

Total Exergy Efficiency (%) Fig. 13. Optimum point.

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

18

19

Fig. 14. Solar share vs. solar time.

1450 1400 1350 1300 1250 1200 1150 1100 1050 1000 950 900

5

6

7

8

9

10

11

12

13

14

15

16

17

Fig. 15. T30 vs. solar time.

factor in optimization of the hybrid plant acting as a final monitor indicating the wellness of the cycle performance. With a more effective air preheater, more air intake, and a lower fuel/air ratio for the hybrid cycle, the inlet stream exergy to the steam generator decreases to 12.47 MW compared to 23.13 MW for the conventional plant. This causes the genetic algorithm to reduce the steam generation rate in the HRSG to 9.69 kg/s (compared to 14 kg/s for the CGAM problem), to achieve a logical design point.

Exergy destruction is another target, since there are many irreversible effects in the process (e.g., heat transfer, friction). Chemical reaction is the main source of exergy destruction in the cycle, with the combustion chamber contributing almost 63% to the total exergy destruction in the conventional cycle. Hybridization reduces the amount of chemical reaction in the combustion chamber, reducing the exergy destruction by half compared to conventional cycle which is 11.64 MW refers to the conventional or hybrid

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M.H. Khoshgoftar Manesh, M. Ameryan / Applied Thermal Engineering 102 (2016) 1300–1313

cycle. Considering the high level of exergy destruction in the solar receivers (34.78 MW), which is mainly due to irreversibility associated with heat transfer and radiation, the total inlet exergy to the hybrid cycle reaches 94 MW, which is 13 MW more than for the conventional cycle and leads to 21.12% lower exergy efficiency. Note, however, that neglecting the solar receivers, the total exergy destruction for the hybrid cycle is 18.69 MW less than for the conventional cycle, demonstrating that the main components in the hybrid plant are more efficient, mainly due to higher efficiencies from optimization. A minimum CO2 optimum has been indicated by optimization based on electricity cost; however a politically driven minimum CO2 optimum has been determined by optimization of CO2. To determine the amount of solar contribution to the products, the solar share factor is evaluated, defined as:

Solar share ¼ Q solar =ðQ solar þ Q combustion Þ The average solar share of the cycle in daytime periods is 35%; the remaining 65% of the required energy is supplied by methane, the backup fuel. Accounting for all operating hours (including nights), the total solar share on an annual basis is 14%. By developing the transient solar field code based on 15-min time steps for the 115th day of the year, which is the day with the greatest available irradiance, the solar share variations with time of day can be determined (see Fig. 14). Plotting the solar preheat temperature (T30 ) transiently (see Fig. 15) shows that after 9:00 in the morning this temperature exceeds the allowed maximum (1300 K). Therefore, mirrors need to be phased out gradually from 9 to 12 AM and then reallocated from 12 to 2:30 PM to maintain the temperature below 1300 K during those periods. Economically, by investing 8533 dollars for each kW of electricity generation for the hybrid cycle, which is almost 30% more than for the conventional plant, the total cost rate of products becomes 20296.90 dollars for each hour of operation compared to 10851.47 for the conventional cycle. Moreover, by subtracting the total capital investment of the conventional cycle from the corresponding value for the hybrid cycle, for each kilogram of CO2 emission avoidance, 2.13 dollar is invested.

6. Conclusion Cuckoo Search algorithm via Levy flights is applied to optimum design of hybrid CHP system. Looking at the CS algorithm carefully, one can observe essentially three components: selection of the best, exploitation by local random walk, and exploration by randomization via Levy flights globally. A hybrid cogeneration plant was developed in order to analyze the performance of the system and compare it with the same structure for a conventional plant. The hybridization was undertaken in the gas turbine section through preheating the compressed air, before combustion, using a solar collector field. The CGAM problem was chosen as the base plant to be modeled in both modes and then for optimization. In the first step both cycles were modeled and then through optimization the optimum design points were chosen. The hybridized plant shifts to the conventional mode performance when the solar irradiance reaches an adequate range, where such adequacy is based on the air mass flow rate and fuel consumption and the target is less fuel consumption rate in the hybrid mode while the air inlet exceeds that for the conventional mode. Regarding this design constraint and a maximum 1000 °C preheating temperature, the share of solar energy in generation of the inlet heat to the turbine is derived to be 35% on average while considering nights this share is 14%. The solar share could be increased by

installing more mirrors in order to maintain the preheat temperature at a plateau of 1000 °C by phasing out them gradually as midday approaches and relocating them after this peak. In the future work, the installed cost of heliostats $/m2 as modeled versus the installed cost of heliostats required to directly compete commercially without subsidies or CO2 mandates, for the price of natural gas assumed. In addition, comparing the assumed ratio of installed heliostat cost to the value of natural gas, to the ratio needed for the hybrid solar to become cost effective. Furthermore, comparing US DOE’s Sunshot Initiative to reduce solar energy costs by 75% from 2010 to achieve grid competitive LCOE of $0.06/kWh.) e.g. reduce installed heliostat costs from $200/m2 to a target of $75/m2 installed by 2020. The Cuckoo Search algorithm has been used the reverence code based on ref [35]. Appendix A. Thermodynamic modeling A.1. Thermodynamic model Chemical Composition of the Combustion Products We assume that the fuel is pure methane and the combustion process is complete according to the reaction:

kCH4 þ ½0:7748N2 þ 0:2059O2 þ 0:0003CO2 þ 0:019H2 O ! ½1 þ k  ½X N2 N2 þ X O2 O2 þ X CO2 CO2 þ X H2 O H2 O Balancing carbon, hydrogen, oxygen, and nitrogen, we determine X N2 , X O2 , X CO2 , and X H2 O are the mole fractions of the components of the combustion products. Specific exergy and energy values Specific exergy of fuel (methane): ef ¼ 51; 850 kJ=kg Specific energy of fuel: in terms of lower heating value: hf ¼ LHV ¼ 50; 000 kJ=kg Specific exergy and energy addition to the water/steam system: Exergy:

e9  e8 ¼ h9  h8  T 0 ðs9  s8 Þ ¼ 909:1 kJ=kg  910 kJ=kg

ðA:1Þ

e9  e8p ¼ h9  h8p  T 0 ðs9  s8p Þ ¼ 754 kJ=kg

ðA:2Þ

Energy:

h9  h8 ¼ 2686:3 kJ=kg  2690 kJ=kg

ðA:3Þ

h9  h8p ¼ 1956 kJ=kg

ðA:4Þ

Specific enthalpy and entropy of substances for pref ¼ 1 bar:

"

 2  1  3 # T b T T d T þ h ðTÞ ¼ 10 H þ a c þ 1000 2 1000 1000 3 1000

3

þ

ðA:5Þ s ðTÞ ¼ Sþ þ a ln



  2  2 T T c T d T þb  þ 1000 1000 2 1000 2 1000 ðA:6Þ

For states where the pressure differs from pref ¼ 1 bar:

pk sðT; pk Þ ¼ s ðTÞ  R ln pref

! with pk ¼ xk p

ðA:7Þ

Here xk is the mole fraction of component K and p is the mixture pressure.

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M.H. Khoshgoftar Manesh, M. Ameryan / Applied Thermal Engineering 102 (2016) 1300–1313

Table A.1 Substance parameters. Substance

Formula

H+

S+

a

b

c

d

Carbon (graphite) Sulfur (rhombic) Nitrogen Oxygen Hydrogen Carbon monoxide Carbon dioxide Water Water Methane Sulfur dioxide Hydrogen sulfide Ammonia

C(s) S(s) N2(g) O2(g) H2(g) CO(g) CO2(g) H2O(g) H2O(l) CH4(g) SO2(g) H2S(g) NH3(g)

2.101 5.242 9.982 9.589 7.823 120.809 413.886 253.871 289.932 81.242 315.422 32.887 60.244

6.540 59.014 16.203 36.116 22.966 18.937 87.078 11.750 67.147 96.731 43.725 1.142 29.402

0.109 14.795 30.418 29.154 26.882 90.962 51.128 34.376 20.355 11.933 49.936 34.911 37.321

38.940 24.075 2.544 6.477 3.586 2.439 4.368 7.841 109.198 77.647 4.766 10.686 18.661

0.146 0.071 0.238 0.184 0.105 0.280 1.469 0.423 2.033 0.142 1.046 0.448 0.649

17.385 0 0 1.017 0 0 0 0 0 18.414 0 0 0

Table D.1 Constants used in the equations of Table A.1 for the purchase cost of the components. Compressor Combustion chamber

C11 = 71.10 $/(kg/s), C12 = 0.9 C21 = 46.08 $/(kg/s), C22 = 0.995, C23 = 0.018 (k1), C24 = 26.4 C31 = 479.34 $/(kg/s), C32 = 0.92, C33 = 0.036 (K1), C34 = 54.4 C41 = 4122 $/(m1.2), U = 18 W/(m2K) C51 = 6570 $/(kW/K)0.8, C52 = 21,276 $/(kg/s), C53 = 1184.4 $/(kg/s)1.2 C61 = 0.78232e6, C62 = 0.01130 C71 = 131$/m2

Gas turbine Air preheater Heat-recovery steam generator Tower Heliostats

eCH ¼ eCH i gas; eCH gas;

phase

eCH liquid;

phase

¼

phase

X

þ eCH liquid;

ðA:11Þ

phase

x0k eCH k þ RT 0

X

x0k ln x0k

¼ x0H2 OðliquidÞ eCH H2 OðliquidÞ

ðA:12Þ ðA:13Þ

where x0k is the mole fraction of the components of the gas phase. For both series of states:

ePH ¼ ðhi  h0 Þ  T 0 ðsi  s0 Þ i

ðA:14Þ

Appendix B. Receiver physical model þ

þ

The constants H ; S ; a; b; c; and d are given for selected substances in Table A.1. Specific exergy of flow at different states:

E ¼ EPH þ EKN þ EPT þ ECH

ðA:8Þ

Note: Kinetic and potential energy effects are ignored. States before combustion (i ¼ 1; 2; 3; 30 ): KN PT CH _ g ðePH Ei ¼ m i þ ei þ ei þ ei Þ CH ei ¼ 0

ðA:9Þ

States after combustion (i ¼ 4; 5; 6; 7): KN PT CH _ a ðePH Ei ¼ m i þ ei þ ei þ ei Þ

ðA:10Þ

B.1. Decision variables In addition to the five decision variable allocated for the conventional cogeneration cycle, the solar preheat temperature, the number of heliostats, and the saturated steam mass flow rate are added decision variables. Therefore, the saturated steam mass flow rate is not a parameter in the hybrid cycle. Parameters Receiver pressure drop: 5% Receiver efficiency (greceiver): 0.5686 Appendix C. Solar energy parameters Solar hour:

Table D.2 Breakdown of total capital investment (TCI). I. Fixed-capital investment (FCI) A. Direct costs (DC) 1. Onsite costs (ONSC)
Purchased-equipment cost
Purchased-equipment installation (33% of PEC)
Piping (35% of PEC)
Instrumentation and controls (12% of PEC)
Electrical equipment and materials (13% of PEC) 2. Offsite costs (OFSC)
Land (0–10% of PEC)
Civil, structural, and architectural work (21% of PEC)
Service facilities (35% of PEC) B. Indirect costs (IC) 1. Engineering and supervision (80% of DC) 2. Construction costs including contractor’s profit (15% of DC) 3. Contingencies (15% of the sum of the above costs) II. Other outlays A. Startup costs (5–12% of FCI) B. Working capital (10–20% of TCI) C. Costs of licensing, research, and development D. Allowance for funds used during construction (AFUDC)

SST ¼ LST  EoT 

  Lloc  Lst 15

ðC:1Þ

EoT ¼ 0:1234  sinðxÞ  0:0043  cosðxÞ þ 0:1538  sinð2xÞ þ 0:0608  cosð2xÞ x¼

360ðN  1Þ 365:24

ðC:2Þ ðC:3Þ

Solar angle:

hs ¼ ðSST  12Þ  15

ðC:4Þ

Sun location in sky:

d ¼ 23:45  sin

  360½284 þ N 365

sinðaÞ ¼ cosðLÞ  cosðdÞ  cosðhs Þ þ sinðLÞ  sinðdÞ sinðas Þ ¼

cosðdÞ  sinðhs Þ cosðaÞ

ðC:5Þ ðC:6Þ ðC:7Þ

M.H. Khoshgoftar Manesh, M. Ameryan / Applied Thermal Engineering 102 (2016) 1300–1313

Hottel equation for calculation of atmospheric efficiency:

sb ¼ a0 þ a1  expðk= sinðaÞÞ

ðC:8Þ

a 0 ¼ 0:4237  0:00821ð6  AÞ2 a 1 ¼ 0:5055 þ 0:00595ð6:5  AÞ2

ðC:9Þ



k ¼ 0:2711 þ 0:01858ð2:5  AÞ2 Normal irradiation at the edge of atmosphere:

Isc ¼ 1353ðW=m2 Þ

ðC:10Þ

   360W DNI ¼ 1 þ 0:034 cos  Isc  sinðaÞ 365

ðC:11Þ

Appendix D. Economic model Tower: The cost function for the tower is defined by Kistler [34] (reference year 1986) (see Tables D.1 and D.2):

PEC tower ¼ ðC61  expðC62  150ÞÞ

ðD:1Þ

Heliostats (mirrors):

PEC ¼ C71  A mir

ðD:2Þ

Receiver:

PEC receiver ¼ 3; 330; 000ð$Þ

ðD:3Þ

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