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Accueil Tous les numéros Volume 81 (2026) Sci. Tech. Energ. Transition, 81 (2026) 7 Full HTML

Table 2

Cost function of all units of Testcase 1.

Unit No. Cost function (Eqs. (5)–(7)) Capacity Limits (MW/MWth)/FOR number
P1 C1(P1) = 0.00028 P 1 2   Mathematical equation: $ {\mathrm{P}}_1^2\enspace $+ 8.1P1 + 550 + |300 sin(0.035 × (−P1))| 0 ≤ P1 ≤ 680
P2 C2(P2) = 0.00056 P 2 2 Mathematical equation: $ {\mathrm{P}}_2^2$ + 8.1P2 + 309 + |200 sin(0.042 × (−P2))| 0 ≤ P2 ≤ 360
P3 C3(P3) = 0.00056 P 3 2 Mathematical equation: $ {\mathrm{P}}_3^2$ + 8.1P3 + 309 + |200 sin(0.042 × (−P3))| 0 ≤ P3 ≤ 360
P4 C4(P4) = 0.00324 P 4 2 Mathematical equation: $ {\mathrm{P}}_4^2$ + 7.74P4 + 240 + |150 sin(0.063 × (60 − P4))| 60 ≤ P4 ≤ 180
P5 C5(P5) = 0.00324 P 5 2 Mathematical equation: $ {\mathrm{P}}_5^2$ + 7.74P5+ 240 + |150 sin(0.063 × (60 − P5))| 60 ≤ P5 ≤ 180
P6 C6(P6) = 0.00324 P 6 2 Mathematical equation: $ {\mathrm{P}}_6^2$ + 7.74P6 + 240 + |150 sin(0.063 × (60 − P6))| 60 ≤ P6 ≤ 180
P7 C7(P7) = 0.00324 P 7 2 Mathematical equation: $ {\mathrm{P}}_7^2$ + 7.74P7 + 240 + |150 sin(0.063 × (60 − P7))| 60 ≤ P7 ≤ 180
P8 C8(P8) = 0.00324 P 8 2 Mathematical equation: $ {\mathrm{P}}_8^2$ + 7.74P8 + 240 + |150 sin(0.063 × (60 − P8))| 60 ≤ P8 ≤ 180
P9 C9(P9) = 0.00324 P 9 2 Mathematical equation: $ {\mathrm{P}}_9^2$ + 7.74 P9+ 240 + |150 sin(0.063 × (60 − P9))| 60 ≤ P9 ≤ 180
P10 C10(P10) = 0.00284 P 10 2 Mathematical equation: $ {\mathrm{P}}_{10}^2$ + 8.6 P10+ 126 + |100 sin(0.084 × (40 − P10))| 40 ≤ P10 ≤ 120
P11 C11(P11) = 0.00284 P 11 2 Mathematical equation: $ {\mathrm{P}}_{11}^2$ + 8.6 P11+ 126 + |100 sin(0.084 × (40 − P11))| 40 ≤ P11 ≤ 120
P12 C12(P12) = 0.00284 P 12 2 Mathematical equation: $ {\mathrm{P}}_{12}^2$ + 8.6 P12+ 126 + |100 sin(0.084 × (55 − P12))| 55 ≤ P12 ≤ 120
P13 C13(P13) = 0.00284 P 13 2 Mathematical equation: $ {\mathrm{P}}_{13}^2$ + 8.6 P13+ 126 + |100 sin(0.084 × (55 − P13))| 55 ≤ P13 ≤ 120
P14 C14(P14) = 0.00028 P 14 2 Mathematical equation: $ {\mathrm{P}}_{14}^2$ + 8.1 P14+ 550 + |300 sin(0.035 × (−P14))| 0 ≤ P14 ≤ 680
P15 C15(P15) = 0.00056 P 15 2 Mathematical equation: $ {\mathrm{P}}_{15}^2$ + 8.1P15+ 309 + |200 sin(0.042 × (−P15))| 0 ≤ P15 ≤ 360
P16 C16(P16) = 0.00056 P 16 2 Mathematical equation: $ {\mathrm{P}}_{16}^2$ + 8.1 P16+ 309 + |200 sin(0.042 × (−P16))| 0 ≤ P16 ≤ 360
P17 C17(P17) = 0.00324 P 17 2 Mathematical equation: $ {\mathrm{P}}_{17}^2$ + 7.74 P17+ 240 + |150 sin(0.063 × (60 − P17))| 60 ≤ P17 ≤ 180
P18 C18(P18) = 0.00324 P 18 2 Mathematical equation: $ {\mathrm{P}}_{18}^2$ + 7.74 P18+ 240 + |150 sin(0.063 × (60 − P18))| 60 ≤ P18 ≤ 180
P19 C19(P19) = 0.00324 P 19 2 Mathematical equation: $ {\mathrm{P}}_{19}^2$ + 7.74 P19+ 240 + |150 sin(0.063 × (60 − P19))| 60 ≤ P19 ≤ 180
P20 C20(P20) = 0.00324 P 20 2 Mathematical equation: $ {\mathrm{P}}_{20}^2$ + 7.74 P20+ 240 + |150 sin(0.063 × (60 − P20))| 60 ≤ P20 ≤ 180
P21 C21(P21) = 0.00324 P 21 2 Mathematical equation: $ {\mathrm{P}}_{21}^2$ + 7.74 P21+ 240 +| 150 sin(0.063 × (60 − P21))| 60 ≤ P21 ≤ 180
P22 C22(P22) = 0.00324 P 22 2 Mathematical equation: $ {\mathrm{P}}_{22}^2$ + 7.74 P22+ 240 + |150 sin(0.063 × (60 − P22))| 60 ≤ P22 ≤ 180
P23 C23(P23) = 0.00284 P 23 2 Mathematical equation: $ {\mathrm{P}}_{23}^2$ + 8.6 P23+ 126 + |100 sin(0.084 × (40 − P23))| 40 ≤ P23 ≤ 120
P24 C24(P24) = 0.00284 P 24 2 Mathematical equation: $ {\mathrm{P}}_{24}^2$ + 8.6 P24+ 126 + |100 sin(0.084 × (40 − P24))| 40 ≤ P24 ≤ 120
P25 C25(P25) = 0.00284 P 25 2 Mathematical equation: $ {\mathrm{P}}_{25}^2$ + 8.6 P25+ 126 + |100 sin(0.084 × (55 − P25)) 55 ≤ P25 ≤ 120
P26 C26(P26) = 0.00284 P 26 2 Mathematical equation: $ {\mathrm{P}}_{26}^2$ + 8.6 P26+ 126 + |100 sin(0.084 × (55 − P26)) 55 ≤ P26 ≤ 120
C1 C27(P27, H27) = 0.0345 P 27 2 Mathematical equation: $ {\mathrm{P}}_{27}^2$ + 14.5 P27+ 0.03 H 27 2 Mathematical equation: $ {\mathrm{H}}_{27}^2$ + 4.2 H27+ 0.031 P27 H27+ 2650 #1
C2 C28(P28, H28) = 0.0435 P 26 2 Mathematical equation: $ {\mathrm{P}}_{26}^2$P28 2 + 36 P28+ 0.027 H 28 2 Mathematical equation: $ {\mathrm{H}}_{28}^2$+ 0.6 H28+ 0.011 P28 H28+ 1250 #2
C3 C29(P29, H29) = 0.0345 P 29 2 Mathematical equation: $ {\mathrm{P}}_{29}^2$ + 14.5 P29+ 0.03 H 29 2 Mathematical equation: $ {\mathrm{H}}_{29}^2$+ 4.2 H29+ 0.031 P29 H29+ 2650 #1
C4 C30(P30, H30) = 0.0435 P 30 2 Mathematical equation: $ {\mathrm{P}}_{30}^2$ + 36 P30+ 0.027 H 30 2 Mathematical equation: $ {\mathrm{H}}_{30}^2$ + 0.6 H30+ 0.011 P30 H30+ 1250 #2
C5 C31(P31, H31) = 0.1035 P 31 2 Mathematical equation: $ {\mathrm{P}}_{31}^2$+ 34.5 P31+ 0.025 H 31 2 Mathematical equation: $ {\mathrm{H}}_{31}^2$+ 2.203 H31+ 0.051 P31 H31+ 2650 #3
C6 C32(P32, H32) = 0.072 P 32 2 Mathematical equation: $ {\mathrm{P}}_{32}^2$+ 20 P32+ 0.02 H 32 2 Mathematical equation: $ {\mathrm{H}}_{32}^2$ + 2.34 H32+ 0.04 P32 H32+ 1565 #4
C7 C33(P33, H33) = 0.0345 P 33 2 Mathematical equation: $ {\mathrm{P}}_{33}^2$ + 14.5 P33+ 0.03 H 33 2 Mathematical equation: $ {\mathrm{H}}_{33}^2$ + 4.2 H33+ 0.031 P33 H33+ 2650 #1
C8 C34(P34, H34) = 0.0435 P 34 2 Mathematical equation: $ {\mathrm{P}}_{34}^2$ + 36 P34+ 0.027 H 34 2 Mathematical equation: $ {\mathrm{H}}_{34}^2$ + 0.6 H34+ 0.011 P34 H34+ 1250 #2
C9 C35(P35, H35) = 0.0345 P 34 2 Mathematical equation: $ {\mathrm{P}}_{34}^2$ + 14.5 P35+ 0.03 H 35 2 Mathematical equation: $ {\mathrm{H}}_{35}^2$+ 4.2 H35+ 0.031 P35 H35+ 2650 #1
C10 C36(P36, H36) = 0.0435 P 36 2 Mathematical equation: $ {\mathrm{P}}_{36}^2$ + 36 P36+ 0.027 H 36 2 Mathematical equation: $ {\mathrm{H}}_{36}^2$ + 0.6 H36+ 0.011 P36 H36+ 1250 #2
C11 C37(P37, H37) = 0.1035 P 37 2 Mathematical equation: $ {\mathrm{P}}_{37}^2$ + 34.5 P37+ 0.025 H 37 2 Mathematical equation: $ {\mathrm{H}}_{37}^2$ + 2.203 H37+ 0.051 P37 H37+ 2650 #3
C12 C38(P38, H38) = 0.072 P 38 2 Mathematical equation: $ {\mathrm{P}}_{38}^2$ + 20 P38+ 0.02 H 38 2 Mathematical equation: $ {\mathrm{H}}_{38}^2$ + 2.34 H38+ 0.04 P38 H38+ 1565 #4
H1 C39(H39) = 0.038 H 39 2 Mathematical equation: $ {\mathrm{H}}_{39}^2$ + 2.0109 H39+ 950 0≤ H39 ≤ 2695.2
H2 C40(H40) = 0.038 H 40 2 Mathematical equation: $ {\mathrm{H}}_{40}^2$ + 2.0109 H40+ 950 0 ≤ H40 ≤ 60
H3 C41(H41) = 0.038 H 41 2 Mathematical equation: $ {\mathrm{H}}_{41}^2$ + 2.0109 H41+ 950 0 ≤ H41 ≤ 60
H4 C42(H42) = 0.052 H 42 2 Mathematical equation: $ {\mathrm{H}}_{42}^2$ + 3.0651 H42+ 480 0 ≤ H42 ≤ 120
H5 C43(H43) = 0.052 H 43 2 Mathematical equation: $ {\mathrm{H}}_{43}^2$ + 3.0651 H43+ 480 0 ≤ H43 ≤ 120
H6 C44(H44) = 0.038 H 44 2 Mathematical equation: $ {\mathrm{H}}_{44}^2$ + 2.0109 H44+ 950 0≤ H44 ≤ 2695.2
H7 C45(H45) = 0.038 H 45 2 Mathematical equation: $ {\mathrm{H}}_{45}^2$ + 2.0109 H45+ 950 0 ≤ H45 ≤ 60
H8 C46(H46) = 0.038 H 46 2 Mathematical equation: $ {\mathrm{H}}_{46}^2$ + 2.0109 H46+ 950 0 ≤ H46 ≤ 60
H9 C47(H47) = 0.052 H 47 2 Mathematical equation: $ {\mathrm{H}}_{47}^2$ + 3.0651 H47+ 480 0 ≤ H47 ≤ 120
H10 C48(H48) = 0.052 H 48 2 Mathematical equation: $ {\mathrm{H}}_{48}^2$ + 3.0651 H48+ 480 0 ≤ H48 ≤ 120

#1–#4 are FORs mentioned in Figures 10a–10d.

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