| Summary: | In this paper, an advanced modus operandi named the -constrained simplex method (ACSM) is deployed to resolve a real-time hydro-thermal-wind-solar power scheduling problem. ACSM is an updated articulation of the Nonlinear Simplex Method (SM) of Nelder and Mead. It has been designed after interbreeding an ordinary SM with some other methods like-evolutionary method, α-constrained method, etc. To develop this technique three alterations in the SM are adopted (i) -level differentiation, (ii) mutations of the worst point, and (iii) the incorporation of multi-simplexes. A real-time multi-objective hydro-thermal-wind-solar power scheduling problem is established and optimized for the Kanyakumari (Tamil Nadu, India) for the 18th of September of 2020. Four contrary constraints are contemplated for this case study (i)fuel cost and employing cost of wind and solar power system, (ii) NOx emission, (iii) SO2 emission, and (iv) CO2 emission. The fidelity of the projected practice is trailed upon two test systems. The first test system is hinged upon twenty-four-hour power scheduling of a pure thermal power system. The values of total fuel cost,emission, emission, and emission are attained as 4707.19$/day, 59325.23 kg/day, 207672.70 kg/day, and 561369.20 kg/day, respectively. In the second test system, two thermal generators are reintegrated with renewable energy resources (RER) based power system (hydro, wind, and solar system) for the same power demands. The hydro, wind, and solar data are probed with the Glimn-Kirchmayer model, Weibull Distribution Density Factor, and Normal Distribution model, respectively. The outturns using ACSM are contrasted with the SM and evolutionary method(EM). For this real-time hydro-thermal-wind-solar power scheduling problem the values of fuel cost, emission, emission, and emission are shortened to 1626.41 $/day, 24262.24 kg/day, 71753.80 kg/day, and 196748.20 kg/day, respectively for the specified interval using ACSM and with SM, these values are calculated as 1626.57 $/day, 24264.67 kg/day, 71760.98 kg/day, 196767.68 kg/day, respectively. The results for the same are obtained as 1626.74 $/day, 24267.10 kg/day, 71768.15 kg/day, 196787.55 kg/day, respectively, by using EM. The values of the operating cost of the solar system, wind system, total system transmission losses, and computational time of test system-2 with ACSM, SM, and EM are evaluated as 8438.76 $/day, 19017.42 $/day, 476.69 MW/day & 15.6 seconds; 8439.61 $/day, 19019.33 $/day, 476.74 MW/day and 16.8 sec; and 8447.20 $/day, 19036.43 $/day, 477.17 MW/day and 17.3 sec, respectively. The solutions portray the sovereignty of ACSM over the other two methods in the entire process.
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