From Uncertain Capacity to Low Carbon Pathways: A Trapezoidal Fuzzy Linear Programming Approach for India’s Power Sector

Abstract

India’s electricity system must expand generation fast enough to support economic growth while also reducing the emissions intensity of the power mix. When future capacity expansion is uncertain and better described by credible ranges than by single-point estimates, fuzzy linear programming becomes a suitable planning tool because it represents feasibility in graded rather than purely binary terms . This paper develops a trapezoidal fuzzy linear programming framework for India’s source-wise electricity capacity planning across coal, gas, solar, wind, hydro, and nuclear technologies. Installed capacity, core expansion bands, and outer support are represented as trapezoidal fuzzy numbers; alpha-cuts are then used to convert the fuzzy model into crisp linear-programming . The model has two goals: maximize annual electricity generation and minimize lifecycle CO2 emissions. Published lifecycle harmonization studies are used to justify the emissions ordering across technologies, with coal and gas remaining substantially more carbon intensive than solar, wind, hydro, and nuclear. Solving the crisp subproblems over  yields a Pareto frontier that clearly shows how the feasible trade space contracts as planning confidence increases . The results indicate that the maximum-generation solution declines from 11,659.03 TWh/year at  to 2,926.61 TWh/year at , while the corresponding CO2 indicator falls from 2.0478 to 1.6792. The minimum-emissions solution remains at the 2,500 TWh/year demand floor, while its CO2 indicator rises from 1.3426 to 1.4480 as the feasible set narrows. These results show that trapezoidal fuzzy linear programming provides a transparent way to connect optimistic and conservative planning assumptions to low-carbon electricity expansion pathways.