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Enabling Technologies for the Integration of Electrical Systems in Sustainable Energy Conversion

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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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