Distributed polygeneration using local resources for an Indian village: multiobjective optimization using metaheuristic algorithm

Abstract

Introduction of renewable energy systems is an imperative need at present. Hybridization of locally available different renewable resources is required due to intermittency of these resources. A multicriteria optimization using cuckoo search algorithm for simultaneous best combination of economy, land use and GHG emission has been carried out for polygeneration with three utility outputs. These are electricity, heat and high calorific value gas. The levelized cost of electricity at 100% reliability of power supply has come out to be 0.1 USD/kWh. For better economy, a minimum plant life of 20 years is desired. This study is with data for a small hilly village of India with mostly poor people. Methodology and results of this study represent optimization of such sustainable energy systems using local resources in specific sites.

Introduction

The consumption of energy and economic development are very closely linked. Developed societies generally have per capita energy consumption higher than that of the developing societies (Toman and Barbora 2003). Presently, the world is mostly dependent on the fossil fuel resources for the supply of energy. Currently, around 78% of electricity need of the world is met by the centralized fossil fuel-based power plants. Out of the fossil fuels, coal is most predominant (around 40%) followed by the natural gas and petroleum, respectively (US Energy Information Administration 2017). There is an expectation of 40% rise in energy consumption by 2040 (USDOE 2016). But fossil fuel reserves are also fast depleting besides having several environmental impacts; most severe is the global warming due to greenhouse gas (GHG) emission. Coal-based power plants emit 50 g-CO₂ equivalent/kWh even with best practices (UK Carbon Footprint 2016).The Intergovernmental Panel of Climate Change (IPCC) has predicted 1.6°–6.3° Fahrenheit rise in global average temperature by 2100 (Climate Change 2016). There is a need to use of renewable sources of energy which are nondepleting and clean in terms of GHG emission. However, these renewable resources are intermittent and dilute in nature. Moreover, limited amount of these resources is available at a particular location depending on the geographical conditions and several other factors including population, livelihood of the local people. So to increase the capacity further technology development with scaled up systems are necessary. Another option is to combine different renewable resources available in a particular locality to increase the capacity of the electricity generation with these limited intermittent resources. This is formally called “hybridization.” The technological development of the renewable energy systems is still developing and scaling up of renewable energy systems for large power supply is yet to be matured. Small-scale distributed systems may be a better option at present. These systems reduce the transmission and distribution (T&D) loss and capacity can be optimized with the available resources and local demand. These systems are also good options to electrify the un-electrified hamlets in India where the extension of national grid is impossible due to terrain conditions or other socioeconomic factors. Integrating other utility outputs in a single unit formally called “polygeneration” makes it even more beneficial and socioeconomically feasible. So these systems need to be designed matching with the local electricity load and other utility requirements. The process integration and generation of useful chemicals enhance the environmental and economic sustainability of systems (Sadhukhan et al. 2015). The design of the polygeneration systems has several objectives as well as constraints and boundary conditions. It has been observed that even in the conventional coal-fired power plants synthesis of other chemicals through the polygeneration route proves to be beneficial both thermodynamically and economically (Ng et al. 2012). So multicriteria optimization is the only option for designing these systems based on the objectives of policy and planning.

Several optimization algorithms exist but all may not be suitable for optimizing a particular system. Hence, the choice of suitable algorithm is also another important issue in this regard. Chauhan and Saini (2016) used the discrete harmony search-based optimization technique for designing the Integrated Renewable Energy System for supplying electricity to some un-electrified villages of the Uttarakhand state of India. Jana and De (2015a) designed a suitable polygeneration system using biomass as the local resource. They have shown that 20% of the primary energy savings is achieved by the process integration. This also leads to the reduction of 25 kt carbon dioxide emission per annum. Kriakarakos et al. (2011) presented a concept of designing a polygeneration system using a battery bank, proton exchange membrane (PEM) fuel cell, PEM electrolyzer and a metal hydride tank, a reverse osmosis-based desalination unit using heat recovery and control system for the supply of power, potable water and hydrogen as the transportation fuel. They have used the Monte Carlo simulation method to take the uncertainty into account. Results of their study show that the polygeneration is technically feasible and profitable with a probability of 90% at present and 100% in the medium term. The use of renewable energy sources like biogas has proved to be efficient economically in UK perspective (Sadhukhan 2014). Ng et al. proposed a polygeneration scheme producing bio-oil. The bio-oil can be treated as an environmentally benign feedstock but at the same time the economic competitiveness of the bio-oil was yet to be judged. The polygeneration scheme along with the electricity generation (Ng and Sadhukhan 2011). Ng et al. showed that the addition of chemicals in addition to the electricity increases the economic competitiveness of the polygeneration system (Ng et al. 2013). Ng et al. has done a comparative study between the biomass gasification combined cycle (BGCC) and biomass gasification fuel cell system (BGFC). It was found that BGFC system provides twice power than that of the BGFC system. It is observed that increasing power generation from BGFC system decreases the power generation efficiency but at the same time the combined heat and power (CHP) efficiency increases (Sadhukhan et al. 2010). Lam et al. (2016) proposed that process integration is an efficient way for energy savings and energy targeting. This paper has emphasized on the recovery of the industrial process heat. Belgana et al. (2013) designed a hybrid renewable energy system with photovoltaic (PV) panel, wind turbine, diesel generator set and a battery bank using the multiobjective optimization technique to optimize the annualized system cost and the reliability of power supply of the system. So economic feasibility and environmental effect assessment have to be assessed before the introduction of a new renewable energy system. So, optimization of a new small-scale renewable energy system is a multicriteria problem. Kriakarakos et al. (2015) designed a polygeneration system using multicrystalline solar module, fuel cell, electrolyzer unit, desalination unit. In this system, the battery can be replaced by a capacitor bank with more intensive use of hydrogen-based systems. Ng et al. (2012) showed that there is a significant improvement in the thermodynamic and economic potential through suitable balanced polygeneration system.

This group of authors is studying polygeneration as a sustainable energy solution from different viewpoints over a period. Starting from component design (Jana and De 2015a, b), performance assessment (Jana and De 2015c), economic feasibility study with real data (Jana and De 2015d), environmental impact assessment (Jana and De 2016, 2017) and finally possible optimization with definite objective functions and real boundary conditions (Ray et al. 2017) are reported in their several publications. In this paper, a multicriteria optimization study is carried out using a metaheuristic algorithm “cuckoo search algorithm (CSA)” to determine a possible optimum solution for a distributed generation with three utility outputs and using local renewable resources only. Real data of a typical Indian village of northern hilly area of the state of Uttarakhand have been studied in this work. Extension of national grid to this area is practically not feasible due to terrain conditions. An estimation of the feasibility and possible optimum solution with multiobjectives and several boundary conditions and constraints are done using CSA. A comparison with the other algorithms like genetic algorithm (GA) and particle swarm optimization (PSO) has also been made. The codes of all these algorithms are developed in MATLAB 2013. Methodology is generic for such optimization problems but, the results may vary depending on the type of system, available data, constraints and boundary conditions. In this case, the site-specific study is done. The multiobjective optimization using a metaheuristic algorithm, i.e., cuckoo search algorithm is carried out here. Obtained results may be useful for the policy makers to decide feasibility of future introduction of such distributed polygeneration system using local resources as a possible future sustainable solution.

Materials and methods

In this paper, a distributed polygeneration system has been proposed to meet the local energy needs of a small village in India. This area has solar, wind, cattle dung (biogas resource) and biomass (straw) resources, which can be used to cater to the energy demand of the local people. The optimum capacities of the various components of the polygeneration system for minimized levelized cost of electricity (LCOE), land requirement and greenhouse gas (GHG) emission are estimated by CSA. The three utility outputs are electricity, cooking gas with high calorific value and heat. Till date, no standardized power dispatch strategy is there for the multigeneration system. However, “ideal predictive power dispatch strategy” is used in this hybrid system. This strategy is used as this proves to be economically the best solution for decentralized power plants using hybrid renewable energy systems (Barley and Winn 1996). The electricity is fed to the local microgrid of this polygeneration to meet the local demand matching the load curve. This village is located in a very cold area with occasional snowfall during winter, moderate rainfall during monsoon and a mild summer (National Institute of Disaster Management 2016). In such villages, there is a need for heating which is included as a utility output in this polygeneration system. Excess hydrogen, which is not used to produce electricity, will be mixed with the biogas and thereby enhancing the calorific value of the biogas. The capacities of the components of the proposed polygeneration system are optimized using CSA with three objectives (1) to minimize the LCOE (2) to minimize land requirement (3) to minimize GHG emission. The multiobjective optimization is carried out using weighted sum method. Comparison has also been made with a few other metaheuristic algorithms like genetic algorithm (GA) and particle swarm optimization algorithm (PSO), with number of iterations constant for all the cases.

System description

The proposed renewable energy-based polygeneration system is modeled using solar PV module, wind turbine, gasifier–gas engine, biogas digester, PEM electrolyzer and a PEM fuel cell as shown in Fig. 1. During the daytime, the solar module generates power which is fed to the local microgrid to meet the local load. The domestic and the agricultural load are predominant in this region as industries are practically nonexistent in such rural areas of India. The seasonal variations of loads along with the electricity generation from the solar and wind resources in the four different seasons are shown in Fig. 2a–d. The excess electricity after meeting the load is fed to the PEM electrolyzer to produce hydrogen, which is stored in the metal hydride tanks. The metal hydride storage is used as it is safer and volume efficient than other hydrogen storage options (Muller and Marmejo 2017). The hydrogen stored is used in a PEM fuel cell to produce electricity and waste heat. The capacity of the electrolyzer is estimated so that it can cater to the maximum load even in the absence of solar energy. So when the load is low, there is excess hydrogen. The excess hydrogen is stored in metal hydride tanks. The stored hydrogen is mixed with the biogas for higher calorific value (CV) of the gas mixture. The resultant gaseous mixture contains hydrogen and biogas in the ratio of 2:3. During night hours, the electrical load is met by the electricity coming from the fuel cell, the gas engine and the wind turbine. The quality of fuel cell water is distilled water standard (Tibaquira et al. 2016). It is again fed back to the electrolyzer.

Fig. 1

Schematic of the polygeneration system

Fig. 2

Load curve and solar radiation pattern of a winter, b rainy, c autumn, d summer

Modeling of the PV system

The solar insolation is incident on the solar panels generating electricity. The module is placed south facing. The total solar radiation on a tilted surface is given by Eq. (1) (Ghribi et al. 2013). The solar system modeling is done in TRNSYS17 as shown in Fig. 3

$$I_{\text{T}} = I_{\text{b}} r_{\text{b}} + I_{\text{d}} r_{\text{d}} + \left( {I_{\text{b}} + I_{\text{d}} } \right)r_{\text{r}}$$

(1)

where I_T is the total radiation on a tilted surface, I_b is the beam radiation on a tilted surface, r_b is the tilt factor for beam radiation, I_d is the diffuse radiation, r_d is the tilt factor for diffuse radiation, r_r is the tilt factor for the reflected radiation. For this case, the reflected radiation is assumed to be negligible.

Fig. 3

TRNSYS model for output of a solar PV module

The tilt factor for the beam radiation r_b for a south facing surface is given by Eq. (2) (Solanki 2009).

$$r_{\text{b}} = \frac{{\text{Cos} \theta }}{{\text{Cos} \theta_{\text{Z}} }}$$

(2)

where θ is the incidence angle of the solar insolation and θ_Z is the zenith angle.

The angle of incidence θ for a south facing surface is given by Eq. (3) (Solanki 2009)

$$\text{Cos} \theta = \text{Sin} \delta \text{Sin} \left( {\varphi - \beta } \right) + \cos \delta \cos \omega \cos (\varphi - \beta )$$

(3)

where δ is the declination angle, β is the slope of the collector, which is equal to the latitude of the place for this paper, φ is the latitude and ω is the hour angle.

The Zenith angle θz for a collector facing south is given by Eq. (4) (Sukhatme 2003)

$$\text{Cos} \theta_{\text{Z}} = \sin \delta \sin \left( {\varphi - \beta } \right) + \cos \delta \cos \left( {\varphi - \beta } \right)\cos \omega$$

(4)

The tilt factor for diffuse radiation r_d is given by Eq. (5) (Sukhatme 2003)

$$r_{\text{d}} = \frac{{1 + \text{Cos} \beta }}{2}$$

(5)

The tilt factor for the reflected radiation is given by

$$r_{\text{r}} = \frac{{\left( {1 - \text{Cos} \beta } \right)\rho }}{2}$$

(6)

where ρ is the albedo.

The instantaneous output voltage $V(t)$ and instantaneous output current I(t) of a PV module is given by Eqs. (7) and (8), respectively (Chauhan and Saini 2016)

$$V\left( t \right) = V_{\hbox{max} } \left[ {1 + 0.0539\log \left( {\frac{{I_{\text{incident}} }}{{I_{\text{standard}} }}} \right)} \right] + \alpha T_{\text{a}} \left( t \right) + 0.02I_{\text{incident}}$$

(7)

where V_max is the open-circuit voltage of the module, $I_{\text{incident}}$ is the solar insolation falling on the module at time t and I_standard is the standard insolation (1000 W/m²), α is the temperature coefficient of open-circuit voltage and $T_{\text{a}}$ is the ambient temperature.

$$I\left( t \right) = \left[ {I_{\text{sc}} + \alpha_{1} T_{\text{a}} \left( t \right) - T_{{\left( {\text{r}} \right)}} } \right] \times \frac{{\left( {I_{\text{incident}} } \right)}}{{\left( {I_{\text{standard}} } \right)}}$$

(8)

where $I_{\text{sc}}$ is the short-circuit current of the module, α₁ is the temperature coefficient of short-circuit current and T_r is the reference temperature.

The instantaneous power of the solar module P_sol(t) is given by

$$P_{\text{sol}} \left( t \right) = I\left( t \right) \times V\left( t \right)$$

(9)

Modeling of the biogas system

The biogas is produced in an anaerobic biogas digester from the cattle dung available in the village. The biogas is mixed with the hydrogen in a ratio of 2:3. The mixing of hydrogen with biogas results to produce a gaseous mixture which has higher CV than biogas. Less than 50% of the gaseous mixture is used by local villagers for cooking purpose and meeting electricity load at night. The excess gas is sold out. The rest is used in the gas engine to produce electricity at night as estimated by Eq. (10).

$$P_{\text{biogas}} \left( t \right) = \frac{{{\text{BG}}_{\text{avail}} \times {\text{CV}}_{\text{bio}} \times \eta_{\text{bio}} }}{\text{OP}}$$

(10)

where ${\text{BG}}_{\text{avail }}$ is the biogas available per day, CV_bio is the calorific value of the biogas, $\eta_{\text{bio}}$ is the efficiency of the gas engine and ${\text{OP }}$ is the operating period (in hours) of the engine per day.

Modeling of the PEM electrolyzer

The instantaneous amount of hydrogen $H_{\text{elect}} (t)$ produced by the PEM electrolyzer is given by Eq. 11.

$$H_{\text{elect}} \left( t \right) = \frac{{E_{\text{elec}} \left( t \right) \times \eta_{e} }}{{{\text{CV}}_{\text{h}} }}$$

(11)

where $E_{\text{elec }} (t )$ is the instantaneous electricity consumed by the electrolyzer, CV_h is the calorific value of hydrogen and η_e is the efficiency of the electrolyzer.

Modeling of the PEM fuel cell

The hydrogen generated by the electrolyzer is stored in a metal hydride tank. Then, the hydrogen is fed to the fuel cell to generate electricity. The electricity generated by the fuel cell E_fc is given by Eq. 12.

$$E_{\text{fc}} = H_{\text{fc}} \times {\text{CV}}_{\text{h}} \times \eta_{\text{fc}}$$

(12)

where $H_{\text{fc}}$ is the amount of hydrogen fed to fuel cell, CV_h is the calorific value of hydrogen and η_fc is the efficiency of the fuel cell.

The waste heat generated by the fuel cell W_fc is given by Eq. 13.

$$W_{\text{fc}} = H_{\text{fc}} \times {\text{CV}}_{\text{h}} \times \frac{{\left( {100 - \eta_{\text{fc}} } \right)}}{100}$$

(13)

where $H_{\text{fc}}$ is the amount of hydrogen fed to the fuel cell, and η_fc is the efficiency of the fuel cell.

Modeling of wind turbine

The instantaneous power output $P_{\text{wind}}$ of a wind turbine is given by Eq. 14.

$$P_{\text{wind}} = 0.5 \times A \times \sigma \times v^{3} \times C_{\text{p}}$$

(14)

where A is the area of the wind front intercepted by the rotor blades, σ is the density of air, v is the wind velocity and C_p is Betz limit. The velocity of wind for this location is taken from NASA Web site as shown in Fig. 4 (NASA Surface Meterology 2017). The density of air is assumed as 1 kg/m³ and the swept area is assumed to be 12.6 m².

Fig. 4

Variation of wind speed over a day in various seasons

Formation of the gaseous mixture

The gaseous mixture is formed by the mixture of hydrogen and biogas in the ratio of 2:3. The calorific value of 1 kg of gaseous mixture, CV_g, is given by Eq. 15

$${\text{CV}}_{\text{g}} = 0.4 \times {\text{CV}}_{\text{h}} + 0.6 \times {\text{CV}}_{\text{bio}}$$

(15)

where CV_h is the calorific value of hydrogen and CV_bio is the calorific value of biogas.

Load curve

The load curve or the electricity demand of this study is taken from the literature as shown in Fig. 2a–d (Kanse-Patil et al. 2011).

Calculation of land requirement

The land requirement L for the entire polygeneration is given by

$$L = L_{\text{sol}} \times {\text{PV}}_{\text{installed}} + L_{\text{bio}} \times {\text{BG}}_{\text{installed}} + L_{\text{wind}} \times W_{\text{installed}}$$

(16)

where $L_{\text{sol}}$ is the land requirement per kW of PV installation as shown in Table 1, PV_installed is the total PV capacity installed, L_bio is the land requirement per kW of biogas as shown in Table 1, ${\text{BG}}_{\text{installed}}$ is the installed capacity of the biogas plant. The land requirement of the fuel cell is neglected as it is very small compared to the other three. It is also assumed that the two biomass-based systems (biomass gasifier and biogas digester) will have a large area shared.

Table 1 Land requirement for solar, biogas and wind systems

Calculation of GHG emission

$$G = G_{\text{s}} \times {\text{PV}}_{\text{installed}} + F_{\text{g}} \times F_{\text{installed}} + G_{\text{d}} \times BG_{\text{installed}} + G_{\text{g}} \times G_{\text{installed}} + W_{\text{g}} \times W_{\text{installed}}$$

(17)

where G is the total GHG emission, $G_{\text{S}}$ is the emission factor of solar module, F_g is the emission factor of fuel cell, F_installed is the installed capacity of the fuel cell, G_d is the emission factor of the biogas digester, BG_installed is the installed capacity of the biogas digester, and G_g is the emission factor of biomass gasifier, G_installed is the installed capacity of the biomass gasifier, W_g is the emission factor for wind turbine and W_installed is the installed capacity of wind turbine. The emission factors are given in Table 2. The emission factors considered here are based on the life cycle assessment of the wind, biomass and the solar systems with on the cradle to grave analysis, i.e., considering the emissions from collecting the raw materials of the product to their final disposal.

Table 2 Emission potential for solar, wind, biogas, biomass and fuel cell systems

Optimization scheme

Cuckoo search

In the present paper, the comparison of cuckoo search algorithm is made with the other metaheuristic algorithm by developing codes in MATLAB 2013. The flowcharts for all the algorithms are shown in Fig. 5. Cuckoo search is a nature-inspired metaheuristic algorithm that has been broadly used for solving complex optimization problems (Tester et al. 2006). CSA is based on the brood parasitism of the cuckoo species. It also uses a balanced composition of a local random walk and global explorative random walks, controlled by a switching parameter p_a. The local random walk can be defined by Eq. (18) (Yang 2014)

$$x_{i}^{t + 1} = x_{i}^{t} + \alpha s \emptyset H\left( u \right)\left( {p_{\text{a}} - \epsilon } \right)\emptyset \left( {x_{j}^{t} - x_{k}^{t} } \right)$$

(18)

$x_{j}^{t}$ and $x_{k}^{t}$ are two different candidate solutions selected randomly by random permutation, H(u) is a heaviside function, ϵ is a random number drawn from a uniform distribution, α is the step size scaling factor and s is the step size. Here, ∅ stands for the entry-wise product of two vectors.

Fig. 5

Flowchart of the optimization scheme using GA, PSO and CSA

On the other hand, the global random walk is carried out by the Lévy flights.

Lévy flights

Lévy Flights are capable of maximizing the probability of resource searches in uncertain surroundings. In optical science, Lévy flight can be defined as a term used to designate the motion of light. Sometimes, light follows a random series of shorter and longer steps rather than traveling in a predictable Brownian diffusion. The shorter and longer steps together form a Lévy flights walk. Most of the natural search processes use Lévy flights. Some bee species perform Lévy flights to find the flowers in a new area. Survey says, by performing Lévy flights more area can be covered than normal random search. Performing Lévy flight is additionally informative than the traditional search methods. Lévy flight is defined by Eq. 19 (Yang, 2014):

$$x_{i}^{t + 1} = x_{i}^{t} \alpha L\left( {s,\lambda } \right)$$

(19)

$$L\left( {s,\lambda } \right) = \frac{{\lambda \varGamma \left( \lambda \right)\sin \left( {{\raise0.7ex\hbox{${\pi \lambda }$} \!\mathord{\left/ {\vphantom {{\pi \lambda } 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \right)}}{\pi }\frac{1}{{s^{1 + \lambda } }} , \left( {s \gg s_{0} > 0} \right); \;\alpha > 0 \;{\text{is the step size scaling factor}} .$$

(20)

In Lévy flights, the Mantegna’s algorithm is used to generate the step size for the determination of search space which is given by Eq. (21)

$$s = \frac{U}{{\left| V \right|^{1/\lambda } }}$$

(21)

where U and V are the two Gaussian distributions and $\lambda$ is the characteristic scale of the problem.

Economic modeling

An economic model is a simplified description of reality, designed to yield hypothesis about the economic behavior that can be tested (International Monetary Fund 2016). The economic model is essential to make the polygeneration socially acceptable to the villagers. The economic performance is assessed along with the thermodynamic performance of the system to judge the overall suitability of the system (Khalid et al. 2017). The various input data for economic modeling are shown in Table 3.

Table 3 Input values for economic calculation

Cost of solar PV

The total cost of PV installation, CP_totall, is given by Eq. 22

$${\text{CP}}_{\text{total}} = {\text{CP}}_{\text{sol}} \times {\text{PV}}_{\text{installed}} \times 1000$$

(22)

where CP_sol is the cost of PV module per watt at the peak of solar radiation and ${\text{PV}}_{\text{installed }}$ is the total installed capacity of the PV module.

Cost of fuel cell

The total cost of fuel cell installation, FC_total, is given by Eq. 23

$${\text{CFC}}_{\text{total}} = {\text{CP}}_{\text{fc}} \times {\text{FC}}_{\text{ins}}$$

(23)

where CP_fc is the cost of fuel cell per watt and FC_ins is the total installed capacity of the fuel cell system.

Cost of biogas system

The cost of biogas systems does not increase linearly with scale. The cost of biogas system is given by Eq. (24) (Jana and De 2015d).

$$C_{\text{eqb}} { = }C_{\text{eqa}} \left( {\frac{{{\text{Capacity}}_{\text{b}} }}{{{\text{Capacity}}_{\text{a}} }}} \right)^{\text{S}}$$

(24)

where $C_{\text{eqb}}$ is the cost of biogas system of capacity “b,” the $C_{\text{eqa}}$ is the cost of capacity of another biogas system “a” and “s” is the scale factor for wet biomass systems.

Cost of electrolyzer

The initial cost of electrolyzer, CE_total, is given by Eq. 25.

$${\text{CE}}_{\text{total}} = {\text{CP}}_{\text{elec}} \times {\text{EL}}_{\text{installed}}$$

(25)

where CP_elec is the cost of electrolyzer per watt and EL_installed is the installed capacity of the electrolyzer.

Cost of hydrogen storage

The cost of hydrogen storage CH_s is given by Eq. 26

$${\text{CH}}_{\text{S}} = H_{\text{d}} \times H_{\text{kg}}$$

(26)

H_kg is the cost incurred to store 1 kg of hydrogen in metal hydride tank and H_d is the maximum hydrogen required per day to meet the night load in a particular season.

Cost of wind turbine

The cost of wind turbine CW_total is given by Eq. 27

$${\text{CW}}_{\text{total}} = W_{\text{installed}} \times {\text{CW}}_{\text{inperkW}}$$

(27)

where CW_total is the total initial investment for the installation of the wind turbine, $W_{installed}$ is the installation capacity of wind turbine and CW_inperkW is the cost of installation of wind turbines per kW.

Cost of gaseous mixture

The cost of 1 kg of gaseous mixture, C_g, is given by Eq. 28

$$C_{\text{g}} = C_{\text{H}} \times \frac{{{\text{CV}}_{\text{g}} }}{{{\text{CV}}_{\text{h}} }}$$

(28)

where CV_g is the calorific value of the gaseous mixture and CV_h is the calorific value of hydrogen.

Annualized initial investment

The annualized initial investment (AI) is given by Eq. 29

$${\text{AI}} = \{ ({\text{CP}}_{\text{total}} + {\text{CFC}}_{\text{total}} + C_{\text{eqb}} + {\text{CE}}_{\text{total}} + {\text{CH}}_{\text{s}} + {\text{CW}}_{\text{total}} + C_{\text{eqbg}} + C_{\text{wh}} ) \times {\text{CRF}}\} + {\text{CH}}_{\text{t}}$$

(29)

where ${\text{CP}}_{\text{total}}$ is the total installation cost of the PV module, CFC_total is the total cost of installation of the fuel cell, $C_{\text{eqb}}$ is the total cost of installation of the biogas systems,${\text{CE}}_{\text{total}}$ is the total initial cost of the electrolyzer, CH_s is the total initial cost of the hydrogen storage systems, CW_total is the total cost for wind turbine installation, C_eqbg is the initial cost for the biomass gasifier system $C_{\text{wh}}$ is the initial cost of the waste heat recovery system and CRF if the capital recovery factor given by Eq. 30

$${\text{CRF}} = \frac{{i\left( {1 + i} \right)^{n} }}{{\left( {1 + i} \right)^{n} - 1}}$$

(30)

where i is the discount rate and n is the economic life of the system. The economic lives of different components may be different and hence annualized cost is considered.

Annualized revenue

The annualized revenue R_y is given by

$$R_{y} = R_{\text{G}} + R_{\text{wh}}$$

(31)

where R_G is the revenue earned from selling gaseous mixture of high calorific value and R_wh is the revenue earned from utility heat.

Levelized cost of electricity (LCOE)

The LCOE is a convenient tool to assess the competitiveness of different generating technologies. The LCOE is calculated taking into consideration the capital cost, fuel cost, fixed and variable operations and maintenance cost (USEIA 2016). The LCOE is given by Eq. 32.

$${\text{LCOE}} = \frac{{{\text{AI}} + {\text{CM}} + {\text{CF}} - R_{y} }}{{E_{t} }}$$

(32)

where AI is the annualized initial investment (i.e., capital cost), CM is the annualized maintenance cost, CF is the annualized fuel cost, i.e., cost of cattle dung for the present system, R_y is the total revenue generated by selling utilities other than electricity. E_t is the total units of electricity generated per year. For renewable energy systems, the maintenance cost and the fuel cost are almost negligible with respect to the initial investment (Budischak et al. 2013). Hence, effects of these are neglected for this study.

Analysis of reliability of power supply

Reliability of electricity supply is an important aspect for the design of any renewable energy system. The analysis of reliability of power supply gives a quantitative idea of the amount of power failure for a renewable energy system. Reliability of power supply can be calculated in different ways. In this paper, this is calculated using the Loss of Power Supply Probability method (LPSP) and Unmet Load (UL) probability method. The LPSP method takes into account both the magnitude of the power failure and the total hours of power failure as shown in Eq. (32). The UL probability method takes into account only the hours of power failure as shown in Eq. (33) (Sinha and Chandel 2015).

$${\text{LPSP}} = \frac{{\mathop \sum \nolimits_{i = 1}^{{i = {\text{n}}}} E_{\text{deficit}} }}{{\mathop \sum \nolimits_{i = 1}^{i = N} P_{\text{load}} }}$$

(33)

where E_deficit is the total electrical energy deficit per year and P_load is the total electrical energy required per year.

$${\text{UL}} = \frac{{\mathop \sum \nolimits_{i = 1}^{i = N} T_{\text{failure}} }}{{\mathop \sum \nolimits_{i = 1}^{i = N} T_{\text{total}} }}$$

(34)

where $T_{\text{failure }}$ is the total hours of electricity failure per year and T_total is the total hours of operation of the plant per year.

Objective function

The main objective of this work is to optimize the system to simultaneously minimize three required inputs as a combined one. These are LCOE (INR/kWh), land requirement (m²) and GHG emission (g-CO₂ equivalent). All these inputs are combined into a single-objective function for simultaneous optimization of this using weighted sum method.

The objective function is given by Eq. (35).

$$S_{\text{obj}} = W_{\text{f}} \times {\text{NF}}_{\text{LCOE}} \times {\text{LCOE}} + W_{\text{L}} \times {\text{NF}}_{\text{L}} \times L + W_{\text{G}} \times {\text{NF}}_{\text{G}} \times G$$

(35)

where $W_{\text{f}}$ is the weighing factor for LCOE, W_L and $W_{\text{G}}$ are the same for land requirement and GHG emission, respectively, and ${\text{NF}}_{\text{LCOE}}$, ${\text{NF}}_{\text{L}}$ and NF_G are the normalization factors for LCOE, land requirement and GHG emission, respectively, to convert the values of each within an order of 10. The values of ${\text{NF}}_{\text{LCOE}} ,{\text{NF}}_{\text{L}} ,\;{\text{and }}\;{\text{NF}}_{\text{G}} \;{\text{are}}\; 1, 10^{ - 3} \;{\text{and}}\; 10^{ - 1} \;{\text{respectively}}.$ Values of three weighing factors are given in Table 4. The values of these weighing factors are decided according to the “priority” of these three for optimization. Higher the priority of optimization, higher is the value of weighing factor. The constraints of optimization are given in Table 4.

Table 4 Constraints for optimization

Results and discussions

In this paper, optimized capacities of the various components of the polygeneration system are shown in Table 5, which is determined by the multiobjective optimization by a program developed in MATLAB 2013. The objective of this optimization is simultaneous minimization of LCOE, land requirement and GHG emission using CSA.

Table 5 Optimized capacity of the components

In the present study, a polygeneration system has been proposed with PV module, wind turbine, PEM electrolyzer, PEM fuel cell, metal hydride tank, biogas digester and biomass gasifier. Electricity is the principal output. The other utility outputs are heat and gaseous mixture of hydrogen and biogas with high CV. Decentralized generation using the renewable sources of energy may be a good option for rural electrification of India. Moreover, electricity is not the only need of the villagers. Apart from the electricity, the people in the villages also need other utilities, say, cooking fuel, utility heating, etc. So if more utilities are obtained from a single efficiently integrated unit and catering to the needs of local people it will be even more beneficial for the villagers. With revenue earned through more utilities, LCOE decreases. Hence, the efficient integration of several processes through polygeneration decreases the LCOE. Effects of the system integration on LCOE are studied in this section.

In the present study, it is observed that the revenue shares of electricity and gas are nearly equal as shown in Fig. 6. The simultaneous production of electricity and hydrogen from the same system helps to accommodate the variation in the load curve of this particular location. When there is excess (i.e., the surplus electricity after meeting the instantaneous load) electricity (i.e., the surplus electricity after meeting the instantaneous load) it is diverted toward hydrogen production through electrolysis of water which is a clean fuel with high calorific value. The hydrogen is mixed with the biogas to yield a rich calorific value gas used for cooking and electricity generation purpose. The surplus of this gas is sold out generating revenue. In the present study, the LCOE is the principal indicator of the economic performance of the polygeneration plant. So, effects of changing various parameters on LCOE are to be studied to assess the suitability of the plant in the long run from the economic point of view. This also helps to identify the principal factors affecting the economic performance of the plant. The effects of various parameters on LCOE are shown in Fig. 7a–h. The various parameters for sensitivity analysis are given in Table 6.

Fig. 6

Pie chart showing the percentage share of annualized income from selling different utilities

Fig. 7

a Variation of LCOE with life of the plant. b Variation of LCOE with percentage of excess biogas utilization. c Variation of LCOE with hybridization of various renewable energy sources. d Adding of different utilities. e Variation of LCOE with Different algorithms. f Variation of LCOE with number of households. g Variation of LCOE with Percentage of increase in initial investment. h Reliability of power supply

Table 6 Variations considered for sensitivity analysis for variation of LCOE

Figure 7a shows the variation of LCOE with the life of the polygeneration plant. The LCOE is high if the life of the plant is below 15 years, and it increases rapidly with decreasing plant life. Higher lifetime of the plant, i.e., more than 15 years decreases the LCOE at a lesser rate, and the LCOE is almost constant if the plant life is above 20 years. So for the better economic operation of the plant, the life of the plant should be 20 years or more.

In India, above 90% of the rural households use firewood as the cooking fuel. Firewood does not burn properly in a conventional way. Rampant use of the firewood for cooking also leads to deforestation causing environmental damages. At the same time, in most of the villages plenty of cattle are available. The cattle dung has a good potential of biogas production. The biogas can be mixed with hydrogen for increasing its calorific value. This high calorific value gaseous mixture can be used as a better cooking fuel. In the present study, about 65% of the total produced gaseous mixture can be used for the electricity generation which is the surplus amount after cooking requirement of the village. This amount of gaseous mixture is termed as “excess” gas in Fig. 7b. Cooking need has more priority than electricity in the villages. Moreover, the biogas production may also vary due to many reasons. If the percentage of use of the gas for electricity generation drops below 60%, then there is an increase in LCOE. This is due to nonutilization of the total capacity of the biogas digester. Moreover, this will lead to increase in size of the fuel cell and wind turbine systems. Hence, the LCOE increases. The renewable sources of energy generally are intermittent in nature. The resources are not available as per the human need with time, i.e., following the load curve. To get reliable power supply using the renewable sources of energy, there are two options. These are either storage and/or hybridization. Most common storage option is to store electricity in a battery. On the other hand, hybridization means to integrate two or more sources of renewable energies like solar, biomass, wind to deliver electricity. Figure 7c shows the variation of LCOE with hybridization of the various sources. Bar chart in Fig. 7c shows the LCOE for only electricity generation (i.e., without other utilities) using different possible combinations from solar PV-battery option and subsequently combining with other possible options. Here, battery indicates storage and other adding options without battery indicate more hybridization. Combinations are plotted from maximum to minimum LCOE. The results of this study show that more hybridization combinations are plotted for maximum to minimum LCOE. The LCOE is the highest for a PV-battery storage system. The LCOE decreases with more hybridization. The least LCOE is obtained when wind–PV–fuel cell–gasifier–biogas digester, i.e., almost all the available renewable energy sources considered for this study are hybridized. The variation of the sizes of the different components like solar PV module, wind turbine with different hybridizations is shown in Table 7.

Table 7 The change of the capacity of the electricity generators on hybridization with other generators

In a polygeneration system, multiple utility outputs are obtained from the same integrated system. Other utilities in addition to electricity are then integrated to study the effect of such integrated system on LCOE in Fig. 7d. Figure 7d shows that the LCOE decreases with adding up of more utilities along with electricity and better process integration. The LCOE is highest for a PV-battery system when the utility output is only electricity with no hybridization. The LCOE decreases to some extent when PV is hybridized with wind. In wind–PV–gasifier system, there are two utilities, i.e., electricity and waste heat. In this case, the LCOE has even decreased more.

Figure 7e shows the different optimized LCOE for different algorithms (like GA, PSO) after forty iterations. The cuckoo search gives the best results because of the global random walks generated by the Lévy flights. Moreover unlike the other algorithms, the CS performs the global convergence, whereas the other algorithms find out the current best solution. For the multimodal optimization, the other algorithms converge to the current best solution without going for the global best solution for a definite search space.

It is necessary to study the suitability of a renewable energy system with respect to the population size of an area. The design of a renewable energy system depends on the number of consumers. The number of consumers generally increases with the number of the households. Hence, the number of households in a village may serve as an indicator of the population. In the present study, the assumed population of the village is 400 persons and the number of households is assumed to be 100. Figure 7f shows the variation of LCOE with the number of households. It is found that for the economic operation of the plant the number of households must be greater than one hundred and fifty. So the increase in the number of households leads to the decrease in LCOE. Moreover, the capacity utilization of the individual renewable energy devices will also increase. In this study, it is seen that the LCOE decreases if the population in a certain area increases.

Figure 7g shows the percentage of increase in LCOE with the increase in initial investment. Electrification of this area with the PV battery systems is considered as the base for comparing the other optimized hybridized multigeneration system. Renewable energy resources are intermittent in nature. Hence to get uninterrupted power supply, hybridization of one or more renewable resources is necessary. The inclusion of more types of renewable energy generators (like SPV, wind turbine) increases the initial capital investment. It has been observed that when the percentage of increase in the initial investment is 15% then the LCOE is decreased by 4%. This area signifies the inclusion of the wind turbine. The initial investment increases with the incorporation of the wind turbine but the LCOE decreases. There is a sharp decrease in LCOE (nearly 9%) when there is a 25% increase in the initial investment. The rise in the initial investment is due to the incorporation of the hydrogen-based systems like PEM electrolyzer and PEM fuel cell. The LCOE decreases as the excess hydrogen mixed with biogas is sold with a good market price. Thus, hybridization can be viewed as a more efficient way of in situ resource utilization.

Reliability of power supply means assured continuity of power supply without failure. Thus, higher the value of reliability of power supply lower is the chance of power failure. The renewable energy systems are intermittent in nature. These energy can be generated when the resources are available but not when it is actually needed. This is one of the most important issues to address for renewable energy introduction replacing the fossil fuel options. So effect of the reliability of power supply on LCOE is studied here. The reliability of power supply is calculated both by “Loss of Power Supply Probability” and “Unmet load” method as shown in Eqs. (33) and (34), respectively. Figure 7h shows that the increase in reliability of above 40% decreases the LCOE. This is also a socially acceptable solution. This is because for the renewable energy systems the running cost is negligible with respect to the initial cost. During the load shedding hours, no revenue is generated but the initial investment is already done. Hence, the LCOE decreases. As reliable uninterrupted power supply assures better social as well as economic solutions, 100% reliability of supply (i.e., no power failure) is considered as the constraint for this optimization.

The unit prices of components may vary due to many technical as well as socioeconomic factors. So to study the suitability of the system in the varying price environment, the sensitivity analysis is performed by varying the price of each of the components of the polygeneration system, i.e., solar module, wind turbine and the fuel cell as shown in Fig. 8. Here, the price of each of the components is varied within a range of 30% of the base price. The present base price of all these components is shown in Table 3. In Fig. 8, it is observed that the percentage of increase in LCOE is most steep with the rise in the cost of PV module per kW. This is because PV is the principal generator of electricity in this polygeneration system. Moreover, the electricity from PV in excess to that for local consumption also generates hydrogen through electrolysis. Hydrogen is mixed with the biogas to form gaseous mixture with high CV. This lowers the LCOE. But if the unit cost of PV module per kW increases then the hydrogen generation also becomes more costly. This also has a positive effect on the rise of LCOE. Next to PV, the LCOE is sensitive to rise in fuel cell prices per kW. This affects as the unit cost of fuel cell is high and it is the second largest electricity producer in this polygeneration system. The LCOE is least affected by the increase in per kW price of wind turbine. This is because the optimized size of wind turbine is much smaller than the other two. The locally available wind resource is also much less than the solar resource. Hence, the size of the wind turbine is relatively smaller.

Fig. 8

Variation of percentage of increase in LCOE with the percentage increase in per kW price of the components

In this study, a multiobjective optimization is carried out considering the minimization of LCOE, land requirement and GHG emission. In this study, LCOE is given the maximum weightage. Figure 9 shows the effect of LCOE if the other factors like land requirement and GHG emission are given topmost priority, i.e., the LCOE at least land requirement and least GHG emission are shown.

Fig. 9

LCOE with different weightage factors to different factors

Conclusion

The extension of national grid across the whole country is difficult due to the terrain conditions and other socioeconomic problems of India. In this context, decentralized generation using locally available resources may provide a solution for the electrification of these scattered hamlets. A system is analyzed in this study with solar PV module, wind turbine, PEM electrolyzer, PEM fuel cell, metal hydride tank, biogas digester (using cattle dung) and biomass (straw) gasifier. Here, the suitable sizes of the components are determined using cuckoo search algorithm for optimum economic operation, land use and GHG emission.

Electricity is not the only utility need of the local villagers. In this study, it is observed that if some other utilities can be integrated with the electricity generation through efficient process integration, the overall system performance improves. Addition of economic values to these utilities leads to economic benefit thereby lowering LCOE. Thus, polygeneration beneficially integrates generation of other utility outputs along with electricity. The LCOE lowers when the plant life is above 15 years. The LCOE decreases with hybridization and the addition of other utility outputs. The LCOE also decreases with the increase in reliability of the power supply above 50% which is a better socially acceptable solution too.

Methodology of this study is generic for multicriteria optimization with decided priority. However, data used are site-specific and results obtained representing optimized solutions may vary both with data used as well as priority decided.