Flexible Fuzzy Goal Programming Approach in Optimal Mix of Power Generation for Socio-Economic Sustainability: A Case Study

: The demand for cost-efﬁcient and clean power energy cannot be overemphasised, especially in a developing nation like India. COVID-19 has adversely affected many nations, power sector inclusive, and resiliency is imperative via ﬂexible and sustainable power generation sources. Renewable energy sources are the primary focus of electricity production in the world. This study examined and assessed the optimal cost system of electricity generation for the socio-economic sustainability of India. A sustainable and ﬂexible electricity generation model is developed using the concept of ﬂexible fuzzy goal programming. This study is carried out with the aim of achieving the government’s intended nationally determined contribution goals of reducing emission levels, increasing the capacity of renewable sources and the must-run status of hydro and nuclear, and technical and ﬁnancial parameters. The result shows an optimal cost solution and ﬂexibility in how increased electricity demand would be achieved and sustained via shifting to renewable sources such as solar, wind and hydro.


Introduction
Environmental sustainability focuses on minimizing the negative environmental impacts of generating electricity based on conventional resources. It can be achieved by increasing production based on renewable energy sources (RES). Therefore, it is composed of several criteria by which power sources have a direct impact on human life, ecological balance, and the environment [1] The ever-increasing CO 2 emissions and the rapid degradation of the environment globally affects environmental sustainability adversely. As a result, policy-makers and researchers are developing interest in, and shifting to, greener manufacturing and the production of electricity via renewable energy sources. Developing countries like India suffer the most from environmental issues due to rapid population growth and lack of adequate resources to harness the potential of RES. Recently, a study was conducted to identify, analyze and rank the predominant barriers restricting India from implementing green manufacturing practices in its small and medium-sized enterprises [2]. The study identified 25 barriers and used different multi-criteria decision-making (MCDM) frameworks to analyze and rank the barriers. The study advocated eco-friendly design in the manufacturing system.
As well as the environmental issue, the COVID-19 pandemic poses challenges globally, especially when developing nations are at a higher risk of damage. The pandemic disrupted regular businesses, supply chain networks, production systems, educational systems and, above all, good governance. Recently, the effects of COVID-19 on the e-commerce of European countries in terms of cyber-security have been analyzed using MCDM tools [3]. The countries' sensitivity to cyber-security and e-commerce performance during the pandemic has been identified and ranked. The study suggests digital transformation to policymakers as a framework for a sustainable environment. Similarly, strategies for managing the adverse effects of the COVID-19 pandemic on the educational sector have been evaluated flexibly using MCDM techniques [4].
Several kinds of research have been ongoing regarding the disruption of the supply chain of food and services during the COVID-19 pandemic. Recently, the challenges and opportunities of the food system and circular economy concerning the COVID-19 pandemic have been studied to pave the way for, and aid, policy designers in enacting environmental sustainability policies [5][6][7]. In all cases, electricity consumption is unavoidable hence the need to devise an optimal mix for the sustainable production of power energy for environmental sustainability development.
In modern times, electricity is among the most important inventions of science for humanity. From home appliances such as fans and toasters, to modern communications and transportation, to the heavy machines used for production in industries, we cannot do without electricity-based technology. India had a population of 1.353 billion people in 2018 alone. It is positioned as the second most populated country globally and the seventh largest economy with a GDP of 2.726 trillion USD in 2018 [8]. However, the electricity consumption per capita was 1122 Kwh in 2017 [9], which is much lower than that of many countries. Electricity shortages are one of South Asia's most significant barriers to achieving development. The power distortion in South Asia causes a four to seven percent lower GDP a year [10]. As of March 2017, Asia's total installed electricity generation capacity, both from utilities and non-utilities, was 377,122 MW and the gross electricity generation was 1,432,358 GWh.
The gross import and export of electricity during 2016-2017 was 5617 GWh and 6710 GWh, respectively. In 2016-2017, electricity available for supply was 1168,317 GWh in, and the estimated electricity consumption was 1,066,268 GWh [9]. The enhancement of India's power sector would be essential to the growth of its economy. Many studies have shown the association between the electricity consumption and the GDP of a country [11][12][13]. The importance of electricity is understandable as electricity consumption serves as an indicator for the socio-economic development of countries [14,15]. With the growth of an economy, electricity demand also grows [See Figure 1]. Because of the scarce fuel resources available to satisfy the demand, additional optimal capacity must be planned [16]. Recently, a two-stage optimization problem was modeled to address hydropower systems and wind parks [17]. The study used mixed-integer linear programming to maximize the system production profits and minimize the imbalances caused by profit reduction penalties. Similarly, wind power production plants have some uncertainties in their production due to the stochastic nature of the operating system during transmission. As such, an optimization model was developed to address the congestions by re-dispatching various cascaded hydropower plants [18]. The study formulated mixed-integer programming to maximize the profit from selling the energy and using a hybrid of quadratic and chance-constrained programming to minimize possible congestions due to re-dispatching the cascaded hydropower plants. More recently, a cooling system with thermodynamic and thermo-economic assessments has been investigated, and energy cost was discovered to be dominant for a single-phase cooling system with a future minimum carbon cost for both systems [19]. Similarly, dynamic mode decomposition has been used to predict the thermal performance of a battery surface [20].
The costs and environmental effects of fossil and nuclear fuels are enormous. Therefore, the need for an optimal mix from various technologies for generating power at a minimum cost cannot be overemphasized. This study tried to assess the cost-optimal additional capacity required by the end of 2021-2022 from conventional and non-conventional energy sources. The study uses flexible fuzzy goal programming to analyze various power generation scenarios for India's sustainable development. This study addresses the UN sustainable development goal 7 (SDG7) related to ensuring affordable, reliable, sustainable and modern energy for all. The goal is interconnected and has synergy with several SDGs such as no poverty (SDG 1), good health and well-being (SDG 3), quality education (SDG 4), clean water and sanitation (SDG 6), decent work and economic growth (SDG 8), sustainable cities and communities (SDG 11), and climate action (SDG 13), among others [21][22][23]. According to [22], "decisions about SDG7 affect humanity's ability to: realize aspirations of greater welfare and well-being, build physical and social infrastructures for sustainable development, and achieve sustainable management of the natural environment." Therefore, achieving SDG 7 will help to realize socio-economic and environmental sustainability. Some benefits of the techniques employed in this study are discussed briefly in the next section.

Benefit of Flexible Fuzzy Goal Programming
Flexible Fuzzy goal programming is one of the distance-based methods. It is an extension of conventional goal programming. One of the significant advantages of such approaches is their computational efficiency. While dealing with multiobjective optimization problems, flexible fuzzy goal programming allows us to stay within an efficient linear programming computational environment. In this method, each objective's aspiration level is taken as unity, regarding their highest degree of achievement goal. The technique helps to solve multiobjective optimization problems with imprecise parameters in a decision-making environment.
Additionally, the approach uses tolerance values, making it more flexible for decisionmakers to realize the range of the solutions they can operate within. In this approach, instead of measuring the achievement of fuzzy objective values directly, achieving membership values of objectives to the highest degree (unity) by minimizing under-deviations is taken into account in a solution search process. All these are incorporated in this research.

Paper Organization
The paper is organized as follows: Section 1 introduces the study background and presents some benefits of the technique used in the study. In Section 2, the relevant literature in the subject area is reviewed, and the research gap established. Section 3 discusses the general multiobjective optimization model followed by the flexible goal programming technique, which the study uses for modeling and solving the problem. The stepwise procedure of the solution method is presented as well. Models related to the levelized cost of energy and its components, such as capital costs, operational costs, and fuel costs, are presented and discussed. Section 4 briefly discusses the sustainable development goals (SDGs) and identifies the SDG 7-goal related to energies and emissions that are crucial to environmental sustainability in the Indian context, based on which the study is carried out. In this section, the Indian Intended Nationally Determined Contribution (INDC), the current scenario of the Indian power sector, the installed capacity of power generation, the Indian electricity generation and consumption, its import and export, and the renewable energy scenarios are all discussed. This section further discusses the state-wise scenario of the power sector and the projections of electricity demand. Section 5 presents the modeling of electrical energy production. The necessary parameters and the system constraints, such as capacity additional targets, renewable energy sources, reserve margin, emissions limits, current energy mixed, and so forth, are discussed. Section 6 presents the results, analysis and discussions, and the article is concluded in Section 7 with research implications and recommendations for decision-makers to implement the findings.

Literature Review
Over the years, researchers have been engaged in optimization, studying and investigating, proposing new methodologies and strategies for finding alternative solutions to the existing and newly emerging problems of human endeavors, for the betterment of the universe. Studies related to the sustainability and development agendas, with respect to India, have been intensive and ongoing. For instance, Rathi [24] and Ghose [25] studied how to promote clean production in the industrial set up of India; Mukherjee [26] considered barriers to the use of energy and the control of pollution with the aim of preserving the environment by the use of cleaner production technologies. The study discovered inconsistency in technology parameters and that they were not reliable for optimizing the eco-friendly casting production problem. Pal et al. [27] studied the process of a device for effectively controlling pollution, developed by the SDC-TERI partnership in India, and discussed measures to replicate and improve the technology for energy efficiency. Narayanaswamy and Scott [28] discussed the lessons derived from cleaner production in textile industries, related to urban and rural environmental interdependency in India.
Unnikrishnan and Hedge [29] analyzed industrial training imparted with the goal of cleaner production. Affordability for cleaner water production was studied by Annala et al. [30], where they used "Reverse Osmosis (RO)" technology to investigate the low cost of water filters in Indian households. The study found that there is active participation in the frugal innovation process by the citizens. Nomani et al. [31] analyzed Indian vision 2030 using the concept of FFGP. Khatun and Ahamad [32] discussed the energy situation in Bangaladesh and analyzed the gap between energy production and usage over 38 years, linking it to the economic growth of the country. McCollum et al. [33] extensively reviewed the linkage between energy and its counterparts related to SDGs.
Similarly, Hassan and Garg [34] studied a system approach for water resource development. Robust optimization techniques have recently been used in sustainability studies [35,36]. Multi-criteria goal programming was used by Gupta et al. [1,37] to analyze the SDGs of India. Recently, a critical review of the application of optimization techniques to the United Nation's SDGs has been conducted [38]. Globally, researchers and decision-makers tend to investigate and proffer solutions to the problem of environmental sustainability [39]. For instance, Yang et al. [40] investigated factors influencing urban sustainability in Beijing and Shanghai in China, and found that service industries have the most substantial consumption of energy and water and CO 2 emissions.
Other similar environmental and electricity regulations have been studied and documented in [39][40][41][42][43][44][45][46][47]. Recently, green energy has been used for providing sustainable economic growth [48,49]. A compact summary of the related work concerning energy studies and environmental sustainability is shown in Table 1. The next section discusses the methodology of this research. -Ranked barriers to implementing greener manufacturing in India Fuzzy MCDM (DEMATEL, ANP, TOPSIS) DAdamo et al. [3].
-Ranking e-commerce in European countries amidst pandemic MCDA and a Likert scale survey Ahmed et al. [4] -Evaluating strategies for managing COVID-19 in education Sector Pareto analysis and rough-DEMATEL Giudice et al. [5].
-Cause-effect analysis of COVID-19 on food security theme popularity metric.

Methodology
In this section, the techniques used for modeling the optimization problem and calculating the levelized cost of energy are discussed and presented. First, a general multiobjective optimization problem is discussed, followed by the specific techniques employed in the study.

Multiobjective Optimization Model
A problem is said to exist if there is a discrepancy between what is and what should be in a real-life situation. Optimization, in simple terms, is finding the best possible desired result(s) out of many available solutions. In an optimization problem, the objective could be single or multiple. A multi-objective problem has more than one objective or goal that is desired to be achieved. It can be a linear or nonlinear function(s) with some constraints or limitations, which can also be linear or nonlinear. For instance, the problem can be about minimizing a certain quantity (say cost) or maximizing a particular value (say profit), or a combination of both. An optimal solution is possible in a single objective optimization depending on the nature of the problem; however, if there is more than one objective, it is a multi-objective optimization problem (MOOP). Naturally, in MOOP, it is impossible to obtain an optimal solution for all the objectives since they could be conflicting. Therefore, a Pareto or a compromise solution is possible. There are different types of models and solutions obtainable in MOOP. The MOOP can be linear or nonlinear depending on the problem's nature and constraints. However, the general MOOP model is presented below: Let a multiobjective programming problem (MOPP) with j objectives functions be given as: where Z j is the set of objectives, g i (x)(≤, =, ≥)b i are m sets of constraints for which b i is the ith resource. Many techniques and approaches exist for solving the MOPP model Equation (1), one of which is flexible goal programming.

Flexible Fuzzy Goal Programming with Tolerance Functions
Fuzzy set theory is a concept to which flexible fuzzy goal programming (FFGP) applies. Fuzzy sets describe the imprecise goals of a decision-maker. These goals are flexible and can be associated with an objective function or constraints. They can reflect a weighting with a value from zero to one or a range of "goal achievement" possibilities. An FFGP allows decision-makers who cannot define goals in a precise manner to express them in a weighting structure, which is not limited. The decision is generally made under four different environments with various conditions. The decision-making takes place in an environment where the DM either has ultimately no knowledge about the environment (ignorance), has complete knowledge (certainty), has little or no knowledge (uncertainty), but can be assigned probabilities and environments in which the DM is competing with the state of nature. Some decisions are simple, while others are very complicated. It is simple when there is precision of the boundaries in the environment, while it is very complicated when the environment is full of uncertainties and vagueness. Fuzzy set theory with imprecise boundaries, developed by Zadeh [51], can handle such vagueness and uncertainty. Zimmermann [52] proposed a fuzzy programming concept for solving multiobjective DM problems, in which both the objectives and the constraints of the problem are considered to be a fuzzy set, a characteristic function (membership) in that set assigns some grades (real values) of membership between one and zero to each of the objectives or goals of the DM. A generalized model for this type of problem (FFGP) can be stated as: Find where g k is the various anticipated future goals, b i is the vector of available resources at hand, and A is the technological coefficient. The symbol is the fuzzy-max type, meaning that Z k (X) should be approximately more than or exactly the same as the level of aspiration g k ; this implies that it can be satisfied by the DM even if it is less than g k at a certain level. The symbol stands for fuzzy-min, meaning that Z k (X) should be less than or exactly the same as the level of aspiration g k approximately, up to an allowable limit (tolerance), while the symbol stands for fuzzy-equal and implies that Z k (X) should be within the level of aspiration g k , which means that it can be satisfied by the DM even if it is less than or greater than g k to a certain level of tolerance. The k-th fuzzy objective is denoted by Z k , and the n-dimensional vector for decision variables is represented by X.
For multi-objective fuzzy goal programming, let g k be the aspiration level set by DM for the k-th objective value Z k (X). Thus, using the method developed by Zimmermann [52], for a maximization problem fo the fuzzy-goal type Z k (X) g k , the membership function for fuzzy-max goals is given as: " While the constraint of a fuzzy model is a subset of vector X with a membership characteristic function λ a ij (x j ): x−→[0,1], given by The Flexible Fuzzy Goal Programming Model can be written as: Find x ∈ X such that it will Maximize λ subject to : where T is the tolerance interval."

Stepwise Solution Procedure for MOPP
We define four linear functions in our study as a multi-objective optimization problem and the following step-wise algorithms are employed for solving the model.
Step 1: Formulate the problem at hand as a multi-objective mathematical model.
Step 2: Obtain the individual optimal solution of the model using any available package, considering one objective at a time.
Step 3: Formulate a pair-wise comparison matrix using the solutions in Step 2, given as: Step 4: Identify the lowest and highest value of each column in Step 3 obtained from Step 2 above and set them as a lower and upper goal, respectively.
Step 5: Construct the membership functions using the FFGP models in Equation (5).
Step 6: Construct a function that will maximize the overall linear additive model of the auxiliary variables defined from the membership function in Step 5 above.
Step 7: Solve for the function in Step 6 using a suitable optimization package and obtain the goal achievement value.

levelized Cost of Energy
The "Levelized Cost" of electricity generation can be defined as "the ratio of the net present value of total capital cost and the total operating cost of a particular plant to the net present value of the net electricity generated by that plant over its operating life" [53,54]. It has not been a reasonable way to quantify the cost economics by simply comparing the electricity generating cost of various RES, such as wind or solar, with that of "conventional sources" such as coal, nuclear or natural gas. Present Net Value (NPV) is one of the critical parameters used to judge the financial viability of the technology; it is the current investment value considering the cost of capital, fuel, as well as other operating and maintenance costs. The LCOE model is given in Equation (6).
where LCOE = levelized cost of energy, I t = initial investment, (OM) t = operating and maintenance charge, F t = fuel cost, r = discount rate, E t = system energy yield, and t = year. The NPV is calculated by determining the annual cash flows from the investment and discounting them to the present time with a specific discount rate. Thus, to compare the costs of generating technologies, the total costs and the load factor for each technology are first considered, and the net present value analysis is then performed. That is the only logical way to evaluate power generation technologies.

Component of levelized Costs
The levelized cost of energy helps with the economic assessment and comparison of different power generation technologies with unequal plant life, capital costs, capacity factor, and fuel costs. Different methods of power generation incur different costs, which include the initial capital cost, operation and maintenance cost and fuel cost (see Table 2).

Capital Costs
Capital costs are the overnight construction costs, including mechanical equipment supply and installation, civil and structural costs, project indirect costs, electrical and instrumentation and control and owners costs [53]. They also include waste disposal and decommissioning costs in the case of nuclear power plants [54]. These costs are lower for gas, wind and solar PV and higher for coal, solar thermal and nuclear.

Operation and Maintenance Cost
Power plants' operating costs include labor and maintenance costs. Unlike the capital costs, the operation and maintenance costs of the plant can vary with the electricity produced. It is low for solar PV, solar thermal and wind, and high for biomass plants.

Fuel Costs
These costs are high for coal, gas and biomass plants, low for nuclear power plants, and zero for many renewable energy sources. Fuel costs can vary arbitrarily over the life of the plants, due to political and other factors such as inflation; therefore, for the present study fuel cost was inflated at 5.72% on a year on year basis.
To calculate the overall cost of the production of electricity from different technologies, various streams of costs are discounted by a discounting factor to net present value. Similarly, yearly energy units produced by different methods are discounted back to net present value. In this study, a discount factor of 10 percent has been used to calculate the net present value of streams of cash outflows and energy units produced. Capital costs, operating and maintenance and fuel costs are applied in Lakh per megawatt installed capacity while electrical energy produced is applied in million U.

Sustainable Development Goals
Member states of the United Nations (UN) adopted the seventeen Sustainable Development Goals (SDGs) in 2015. The SDGs serve as a global action against poverty, hunger, AIDS and discrimination, and to ensure that all people enjoy peace and prosperity by 2030 for balanced and sustainable social, economic and environmental development [55]. The SDG 7 agenda is determined to ensure the affordability, reliability, and sustainability of energy for the benefit of all. Secure energy access is linked with various social and economic development goals such as alleviating poverty, education, health, improving industrialisation, providing infrastructure for communication, and mitigating climate changes. In India, NITI Aayog is saddled with the responsibility of ensuring the SDG implementation, while the "Ministry of Statistics and Programme Implementation (MoSPI) is evolving the related national indicators" (Economic survey, 2017). Therefore, GOI needed to enrich the existing policies and intended to introduce more efficient and cleaner technologies, promote renewable energy, reduce carbon emissions from different sources, promote energy efficiency in the economy, develop resilient climate infrastructure, Implement programmes of afforestation, enhance climate resilience and reduce vulnerability to climate change.

Current Scenario of the Indian Power Sector
In India, electricity generation, transmission, distribution and trading are currently governed by the Electricity Act of 2003. The act promotes the development of the power industry by promoting and encouraging competition, protecting consumers' interests, ensuring electricity supply, electricity bill rationalisation, transparent subsidies policies, and promoting efficient electricity policies. The Central Electricity Authority (CEA) advises the government on policy matters regarding the country's electricity system. It has a constitution under section 3(1) of the "Electricity Supply Act 1948", which was superseded by section 70(1) of the "Electricity Act 2003". The central electricity regulatory commission is a statutory body with "quasi-judicial status," functioning under section 76 of the Electricity Act 2003 for rationalisation of the electricity tariff. Many state electricity regulatory commissions are also working for the development of power sector in the respective states. The Appellate Tribunal for Electricity APTEL was established in 2005 to appeal against the orders of the arbitrating officer or central and state electricity regulatory commissions under the Electricity Act 2003. In collaboration with the states, CEA (the 'Central Electricity Regulatory Commission') and other stakeholders, the Government of India (GOI) issued a revised tariff policy in 2016. The electricity is generated from conventional sources of energy such as coal and lignite, hydro, nuclear and natural gas power generation as well as from non-conventional RES such as solar, wind, biomass, small hydro, tidal, geothermal, waste to energy and hydrogen/ fuel cells, among others. The CEA, the Ministry of Power and the GOI consider the principles of sustainable development in the power sector and the development of generation capacity to meet the demand pattern, varying demand, efficient use of resources, availability of fuel and integration of Non-Dispatchable Renewable Energy Sources (NDRES) like wind and solar, during the planning process for electricity generation capacity addition [56]    The Ministry of Power issued import/export (Cross Border) guidelines for electricity in 2018 [58]. After adding the net import and purchase of electricity from non-utilities, the electricity available for supply in 2016-2017 was 1,168,317 GWh, while the loss of electricity due to transmission was 21.30%, a much higher loss rate than other countries.

Consumption of Electricity
According to the report of [58,59], India has become the third-largest producer as well as consumer of electricity in the world. In 2016-2017, the estimated electricity consumption was 1,066,268 GWh. However, the average consumption of electricity per capita in India was only 1122 Kwh in 2017 [9], which is much lower than that of the world's average per capita electricity consumption (see Figure 6). Despite having a lower tariff, the per capita electricity consumption of India is much lower compared to many other countries. Of India's electricity consumption, industry consumed 40.01 percent of the total, followed by the domestic sector which consumed 24.32 percent, agriculture with a consumption of 18.33 percent and the commercial sectors with 9.22 percent, respectively as shown in Figure 7.

Renewable Energy in India
India is among the countries with the most significant production of energy from renewable sources. Including hydro, as of March 2017, renewable energy accounts for 31.12 percent of the total installed capacity from the utility in the country, while renewable energy sources other than hydro accounted for 57,244 MW, which is 17.51 percent of the total installed capacity. Wind power capacity was 32,280 MW, solar accounted for 12,288.83 MW, biopower accounted for 8295.78, and the small hydro plant has a capacity of 4379.86 MW (see Figure 8). A total of 175 GW has been targeted by the Government of India for installed capacity from RES by March 2022. The additional capacity anticipated from RES during 2022-2027 has been considered to be 100,000 MW, of which 50,000 MW will be from solar, 40,000 MW from wind, 7000 MW from biomass and 3000 MW from small hydro, respectively, to reach a target of 175 GW RES by 2021-2022 and 275 MW by 2027. There is a huge potential for power generation in India from RES. The total potential for generating renewable power in India in 2017 was projected to be 1,001,132 MW. These include 649,342 MW from solar, 302,251 MW from wind, 21,134 MW from small-hydro, 18,601 MW from biomass, 7260 MW from "bagasse-based" cogeneration in sugar mills and 2554 MW from waste to energy. The detailed estimated potential for renewable energy in India is presented in Section 4.3.

State-Wise Scenario of the Power Sector
The installed state-wise and region-wise capacity of power generation as of 31st March 2017 and the per capita power consumption during 2016-2017 have been reported. Furthermore, the state-wise and region-wise projected energy requirement and peak demand for 2021-2022 and 2026-2027, and the estimated potential of renewable power, were also investigated. Dadra and Nagar Haveli have the highest electricity consumption per capita with 15,783 Kwh, while Bihar has the lowest consumption in the country, with 272 Kwh for 2016-2017. In India, the per capita power consumption was 1122 Kwh in 2017, far lower than many developed countries. Maharashtra has the highest projected energy requirement and peak demand for 2021-2022 and 2026-2027, followed by Uttar Pradesh, Tamil Nadu and Gujarat. Rajasthan has the highest share of the estimated potential of renewable power generation, at about 16.21 percent (i.e.,162,326 MW), followed by Gujarat with 12.17 percent (i.e., 121,791 MW) and Jammu and Kashmir with 11.27 percent (i.e., 112,800 MW), mainly from solar power potential.

Electricity Demand Projections for India
Various agencies and investigators have made projections for energy demands in India; these reports have a substantial spread in energy demand forecasts. According to the World Bank, with expected GDP growth at an average of 7 percent every year, demand for electricity in India would be almost tripled between 2018 and 2040 [11]. In another report, nine electricity demand projections were generated for three scenarios of GDP growth and three levels of energy efficiency. Aggregate demand could grow from 949 TWh in 2015 to 2338 TWh in 2030 [60]. The Energy Resources Institute (TERI) presented the future electricity mix in its report in 2017, based on two scenarios: a 'High Renewables Scenario (HRES)' and a 'Low Renewables Scenario (LRES)'. In the HRES, the renewable energy capacity increases by 125 GW in 2021-2022, 225 GW in 2025-2026 and 803 GW in 2029-2030 from 50 GW, respectively. The LRES is based on a lower trajectory of renewables; here, capacity addition was taken to be 75 GW during the first five years and 100 GW in the five years after that [61]. The aggregate projected electricity energy requirement in MU and peak demand in megawatt are presented in Table 3. The national electricity plan surveyed the periods of 2021-2022 and 2026-2027 to identify the optimal capacity mix based on the demand of electricity, considering various initiatives by GOI, such as RES capacity targets by 2022 with committed capacity. The present study suggests an optimization model intending to minimize the cost of generation considering various other constraints.

Electrical Energy Production Modeling
In this section, we discuss the constraints and parameters of modeling the electrical energy system.

Constraints for Electric Energy Production
The optimum mix of electricity generation can be viewed as an optimisation problem, where the objective is to minimise the operating cost of the existing plants and levelized cost of capital and operating new generating stations satisfying a different set of constraints or limitations in the system, which include: " "The various decision variables of the problem are as follows: X 1 = Installed Capacity of Hydro X 2 = Installed Capacity of Coal X 3 = Installed Capacity of gas X 4 = Installed Capacity of nuclear X 5 = Installed Capacity of solar thermal X 6 = Installed Capacity of solar PV X 7 = Installed Capacity of Wind X 8 = Installed Capacity of Biomass X 9 = Installed Capacity of Small Hydro.

Renewable Capacity Addition Targets Fixed by Government
The GOI recently set a target to achieve 175 GW capacity installed from RES by March 2022 (see Table 4). Additional capacity anticipated from RES during 2022-2027 has been considered to be 100,000 MW, of which 50,000 MW would be from solar, 40,000 MW from wind, 7000 MW from biomass and 3000 MW from small hydro, respectively, to reach a target of 175 GW RES by 2021-2022 and 275 MW by 2027 (see Table 4).

Must Run Status for Renewable Energy Sources
Must Run Renewable Energy Sources, such as solar, wind, nuclear and hydro projects, followed by gas being given priority, are considered the "must run projects" based on their potential. During 2017-2022, the additional capacity of hydro is estimated to be about 6823 MW, and that of nuclear about 3300 MW, while hydro is projected to total 12,000 MW, and the additional capacity of nuclear is projected to total 6800 MW in the years 2022-2027 (see Table 5). Renewable capacity is also considered a "must-run" capacity.

Loss on Load Probability and Energy Not Served
This is the probability of an electricity system failing to serve the peak load. It can be described as the proportion of days or hours in a year when the available capacity generated is insufficient to meet the peak demand. Energy Not Served can be expressed as a fraction of the total energy required, which is expected not to be supplied to the consumers by the electricity system. It is the unmet energy demand in the number of hours in a year. LOLP and ENS are used as reliability criteria for electricity systems. LOLP of 0.2 percent and ENS of 0.05 percent are adopted for electricity planning in India.

Provision for Reserve Margin
Future electricity demand is challenging to forecast with accuracy, therefore, as a simple strategy, a capacity with more supply than may be required is maintained as it would take years to build new power generation capacity. "Reserve margin = (Capacity − Demand)/Demand, where capacity is the expected maximum available supply and demand expected peak demand". A 5% spinning reserve for conventional plants is required as per the National Electricity Plan in India.

International Commitments by India
The Indian Government is committed to achieving "energy autonomy and to provide clean, affordable, reliable and sustainable power for all". The GOI has made the international commitment (INDC) to have at least 40 percent electric power capacity installed from non-fossil fuel-based sources cumulatively by the year 2030 and to reduce the intensity of its GDP emissions by 33 percent to 35 percent by the year 2030 from the levels in 2005. The non-fossil fuel energy sources include hydro, nuclear and RES. The Government of India recently set a target of achieving 175 GW installed electricity capacity from renewable energy sources (RES) by March 2022. More emphasis is given to developing a non-fossil fuel-based generation of power, that is, hydropower, to the greatest extent possible, shifting towards more efficient supercritical technologies for coal-based power plants.

Emission Limits
The Indian government has made an international commitment (INDC) to reduce its GDP emission intensity by 33 to 35 percent by 2030 from the levels in 2005. Therefore, the installed capacity of thermal sources (coal, gas, diesel and ignite) of electricity should be those with smaller emissions than the prescribed emission limit for the government's INDC goal for emissions intensity. The estimate of the total emission of CO 2 from the "grid-connected" power stations during 2005 was 462 million tonnes. The emission of CO 2 resulting from the power sector was estimated to reach 1026 million tonnes at the end of 2021-2022 and 1173 million tonnes at the end of the year 2026-2027, respectively. Emission intensity is likely to reduce by 40.51 percent and 53.65 percent, respectively, at the end of 2021-2022 and 2026-2027 from the 2005 level [62]. In the year 2005, the emission intensity in India was 0.015548 kg CO 2 /GDP. The GDP in 2005 was Rs 2971464 crore at factor cost [1,31,37]. For the present study, 2005 has been taken as the base year, and GDP at factor cost for 2021-2022 and 2026-2027 has been projected, assuming an annual GDP growth rate of 7 percent. Available GDP of 2013-2014 at the base price of 2005 was Rs 5,741,791 crore [63]. Projected GDP for 2021-2022 is Rs 9,865,466 crore, and for 2026-2027 it is Rs 13,836,826 crore (see Table 6). Emission intensity in 2005 was 0.015548 kg CO 2 /Rs GDP [64]. The Government of India has made an international commitment (INDC) to reduce the emissions intensity of its GDP by 33 to 35 percent by the year 2030 from the 2005 level. For the present study, we have assumed achievement of this target by 2026-2027. Therefore, in 2026-2027 the emission intensity should reduce to 0.010062 kg CO 2 /Rs GDP. Therefore, total allowed emissions should be 0.010062 * 98, 654, 660, 000, 000 = 992, 663, 188, 920 kg for the year 2021-2022 and 0.010062 * 138, 368, 260, 000, 000 = 1, 392, 261, 432, 120 kg for the year 2026-2027. Table 7 shows CO 2 emission factors for different power generation systems [50,64]. A coal-based electricity generation system has a substantial CO 2 emission factor. As the installed capacity of power generation is primarily coal-based, coal is a significant source of emitting carbon dioxide in India. Therefore, if RES usage increased and thermal efficiency improved, the CO 2 emissions in India would be reduced significantly.   Table 5) while 47,855 MW are under-construction and to be completed during 2017-2022 [62]. Therefore, the likely capacity of coal would be 217,302 MW in 2021-2022. The various cost components of electricity production are the capital cost, operation and maintenance cost, and fuel cost. The cost of electricity production also depends upon specific fuel consumption, capacity factor, auxiliary consumption and plant life (see Table 2). In the current study, the technology-specific and overall cost of electricity was computed with the help of a levelized energy formula Equation (6).

Mathematical Model Formulation
In this section, we formulate three models with the objectives of minimizing the levelized cost of electricity, minimizing the total present value of the cost of energy, and maximizing the present value of total energy produced. In order to optimise the system cost, we introduce installed capacities as variables with the respective costs of the generation technologies and specified constraints. LCOE is calculated by dividing all expected "technology lifetime costs by the total energy production" throughout its lifetime. The present value of the cost of energy is computed as the ratio of the present value of the cost of the installed capacity to the present value of energy produced over the lifetime of the plants, while the last objective is calculated as the present value of total energy produced over the lifetime of different plants. The complete mathematical formulation is presented in Equatinos (7) 12, 289 ≤ X 5 + X 6 ≤ 100, 000 169, 447 ≤ X 2 ≤ 217, 302, 26, 167.01 ≤ X 3 ≤ 26, 573.01, 6780 ≤ X 4 ≤ 10, 080, 32, 280 ≤ X 7 ≤ 60, 000, 8295 ≤ X 8 ≤ 10, 000, 4380 ≤ X 9 ≤ 5000.
Equation (7) is related to optimizing the levelized costs of energy by individual technologies. Equation (8) is related to optimizing the levelized costs of energy by all technologies. Equation (9) is related to optimizing the present value of energy by all technologies. These Equations (7)-(9) are derived from Table 2.
The constraints of the above optimization model are explained as follows: Constraint Equation (10) is related to the unit production of electricity in a year derived from Tables 2 and 3. Constraint Equation (11) is related to CO 2 emissions limit during a year. The coefficient of the constraint is derived from Section 5.1.6, Tables 2 and 7. Constraint Equation (12) is related to non-fossil fuel derived from Section 5.1.5. Constraint Equation (13) is related to solar installed capacity derived from Table 4. Constraint Equation (14) is related to hydro installed capacity derived from Tables 5 and 8. Constraint Equation (15) is related to coal installed capacity derived from Section 5.1.6. Constraint Equation (16) is related to gas installed capacity derived from Tables 5 and 8, respectively. Constraint Equation (17) is related to nuclear-installed capacity derived from Tables 5 and 8, respectively. Constraint Equation (18) is related to projected wind installed capacity derived from Table 4. Constraint Equation (19) is related to projected bio-power plant capacity derived from Table 4. Finally, constraint Equation (20) is related to projected small hydro capacity derived from Table 4.

Results Analysis and Discussions
This study was carried out using the flexible fuzzy goal programming (FFGP) approach to find out the optimum cost solution for electricity "system expansion" for the study period from 2016-2017 to 2021-2022. The model proposed determines the optimal cost expansion that will guarantee the optimal mix of the capacity generation for all the years until 2021-2022, considering all the input parameters (financial/technical) for the study period. The optimal mix of installed capacity by the end of the year 2021-2022 is given in Table 9. The FFGP model has selected the target installed capacity of hydro, nuclear, solar, wind, biomass and small hydro due to the reduction in cost and CO 2 emissions. The model does not select any new coal power plants apart from the existing projects. It can be observed that RES installed capacity, including solar and wind, will become 160,000 GW by the end of 2021-2022, which is more than 35 percent of the total installed capacity of 447,027.83 GW. In contrast, energy from non-fossil sources will be 236,381.4 GW by the end of 2021-2022, which is more than 52 percent of the total installed capacity of 447,027.83 GW. Capacity expansion for coal-based plants is not significant as compared to the solar and wind capacity addition.
The optimal gross electricity generation during the year 2021-2022 is 1,597,715 MU, comprised of 983,611 MU from thermal, 177,507 MU from solar, 151,757 MU from wind, 155,504 MU from hydro, 54,584 MU from nuclear and 55,226 MU from biomass and 19,526 MU from small hydro, as shown in Table 10. It can be noticed from the results above that the installed capacity of non-fossil fuel-based plants, including solar, wind, biomass, hydro and nuclear-based, is likely to be about 50 percent of the total installed capacity. It contributes around 35 percent of the gross electricity generation in the year 2021-2022. The levelized cost of electricity at this optimal solution would be Rs 51.53 lakh per MU or Rs. 5.15 per Kwh. Furthermore, we introduce different tolerance values to the FFGP model to obtain the optimum cost solution for electricity system expansion for the study period of 2016-2017 to 2021-2022. We considered both technical and financial input parameters and a tolerance of one percent to ten percent for increasing the projected demand and installed capacity of solar, hydro, wind and small hydro. The optimal mix of installed capacity with tolerance level is given in Table 11. As evident from Table 11, the projected demand and installed capacity of renewable sources of electricity increased by one percent to ten percent tolerance throughout the solution cases. The optimal solutions give increased installed renewable sources of electricity that is hydro, solar and small hydro. In contrast, it does not increase non-renewable sources such as gas, nuclear and biomass. The optimal solution also indicated a slight increase in the installed capacity of coal; however, it does not exceed the existing and under-construction plants, implying that no new plant is required. Table 12 shows that the levelized cost for an optimal electricity system at a different level of tolerance, ranging from one percent to ten percent, decreases as the demand increases. This implies that increased electricity demand can be met with renewable energy sources by increasing hydro, solar PV and small hydro, which have lower levelized costs than non-renewables such as gas, nuclear and biomass, which have a higher levelized cost.

Managerial and Practical Implications
Results of the study indicate that flexible fuzzy goal programming can be implemented to meet energy demand in the future, at the same time achieving various national goals and international commitments. The results and methodology of the study can be used by researchers and governments to further the research in the field of the cost-production optimization of energy. There are various sources of energy generation; however, some are costly and have a highly negative impact on environmental sustainability. Therefore, from the managerial perspective, such sources are not the most desired. Currently, most of the energy produced by the GOI is based on hydro and coal, and their installed capacity can meet the Indian demands up to 2022. However, from 2022 onwards, there will be a high demand for electricity power due to the increasing population. As such, this study suggests shifting to renewable energy sources. The study further suggests the rates of shifting from non-renewable to renewable sources at every step. The tolerance values shown in Table 11 provide the optimal mix for electricity generation from the various technologies. This concept will help the government and policymakers to gain insight into what amount is required from every technology to optimally generate electricity for the sustainable development of India. The study balanced the three tiers of the SDGs-social, economic and environmental issues.

Conclusions and Recommendations
India is determined to ensure the affordability of clean energy for the benefit of all and intends to reduce CO 2 intensity by adopting low-carbon technologies, as evident from the INDC submitted to the UNCC and their various targets for RES. It is observable from Tables 11 and 12 that, with an increase of projected demand from one percent to ten per cent, the capacity expansion for "coal-based" plants is not significant as compared to renewable energy capacity addition; also the levelized cost decreases as the electricity demand increases. Although India has made sound progress towards a mix of cleaner energy as recognized by the international community [65], the following recommendations are vital for accelerating India's progress towards attaining cost-efficient and clean electricity generation while simultaneously achieving its international commitments and financial and technical constraints. • The optimal allocation of installed capacity among different technologies in Table 9 can be adopted to meet the projected demand for electricity; • For any further increase in demand, the allocation of different electricity plants can be made based on the optimal solution in Table 11; • Increasing electricity demand should be made by shifting allocations towards renewable energy sources, especially solar, wind and hydro; • A less-costly decommissioning method can be adopted for plants, especially for the nuclear plant; • Government should install solar panels on the roof-tops of government offices and encourage individuals to use a solar panel for electricity generation for their personal use; • Government should reduce the dependency on costly imported coal and explore and use domestic coal reserves for running existing coal plants.
This research studied energy policy choices and addressed issues related to electricity generation (SDG 7), and will enhance the achievement of several SDGs for environmental sustainability in many ways.

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Shifting from fossil fuels to renewable energy sources may lower carbon dioxide emissions, which furthers climate change mitigation goals (SDG13); • Ensuring efficient energy access to poorer citizens and deploying large scale renewable sources will positively impact the SDG1 goal of alleviating poverty and all its ramifications; • Energy efficiency will help achieve the sustainability of cities (SDG11), and with smart cities, road traffic accident risks will reduce drastically, improving peoples' health (SDG3); • The provision of access to efficient and affordable energy will create employment opportunities for men and women who will be engaging in hairdressing and digital services (SDG5). It will also improve the quality of education via access to laboratories, internet facilities and modern technologies, helping the necessary flourishing of interdisciplinary research (SDG 10). Funding: The first author is thankful to Saudi Electronic University, Riyadh, Saudi Arabia, for providing a financial assistant to carry out this research.