You are asked to plan additions to power generating capacity and energy conserva
ID: 342573 • Letter: Y
Question
You are asked to plan additions to power generating capacity and energy conservation for an electric utility over the next 40 years. These additions will accommodate both growth in power demand and replacement of old generating plants. Forecast growth in power demand, which includes planned closures and replacement of old plants, is given in Table 1 for 5-year intervals. Table 2 lists the generating units being considered. Note that all units are required to accommodate demand in the year 2060 Table Year 2020 2025 2030 2035 2040 2045 2050 2055 2060 Growth above Present (M 1,000 1,600 2,200 2,600 3,000 3,500 4,000 4,600 Table 2:Type of Unit No. Units Capacitv/unit Cost/unit Coal Gas Turbines Wind Turbines Energy Conservation 10 10 4 500 MW $400 million 100 MW$100 million 50 MW 150 MW$100 million $75 million (a) Formulate this problem as an integer programming problem, minimizing the present value cost of expansions over this period. Specify the decision variables, objective function, and constraints. Assume a 5% inflation-adjusted discount rate.Explanation / Answer
(a) Decision variables: Let Ci,Gi,Wi,Ei be the number of units of Coal, Gas turbines, Wind turbines, and Energy conservation type to be added in year i, where i {1,2,3,4,5,6,7,8,9} for the nine years at 5-year interval starting with year 2020, considering 2020 as the base year
Max (400C1+100G1+75W1+100E1)/1.05^0 + (400C2+100G2+75W2+100E2)/1.05^5 + (400C3+100G3+75W3+100E3)/1.05^10 + (400C4+100G4+75W4+100E4)/1.05^15 + (400C5+100G5+75W5+100E5)/1.05^20 + (400C6+100G6+75W6+100E6)/1.05^25 + (400C7+100G7+75W7+100E7)/1.05^30 + (400C8+100G8+75W8+100E8)/1.05^35 + (400C9+100G9+75W9+100E9)/1.05^40
s.t.
500C1+100G1+50W1+150E1 >= 0
500(C1+C2)+100(G1+G2)+50(W1+W2)+150(E1+E2) >= 1000
500(C1+C2+C3)+100(G1+G2+G3)+50(W1+W2+W3)+150(E1+E2+E3) >= 1600
500(C1+C2+C3+C4)+100(G1+G2+G3+G4)+50(W1+W2+W3+W4)+150(E1+E2+E3+E4) >= 2200
500(C1+C2+C3+C4+C5)+100(G1+G2+G3+G4+G5)+50(W1+W2+W3+W4+W5)+150(E1+E2+E3+E4+E5) >= 2600
500(C1+C2+C3+C4+C5+C6)+100(G1+G2+G3+G4+G5+G6)+50(W1+W2+W3+W4+W5+W6)+150(E1+E2+E3+E4+E5+E6) >= 3000
500(C1+C2+C3+C4+C5+C6+C7)+100(G1+G2+G3+G4+G5+G6+G7)+50(W1+W2+W3+W4+W5+W6+W7)+150(E1+E2+E3+E4+E5+E6+E7) >= 3500
500(C1+C2+C3+C4+C5+C6+C7+C8)+100(G1+G2+G3+G4+G5+G6+G7+G8)+50(W1+W2+W3+W4+W5+W6+W7+W8)+150(E1+E2+E3+E4+E5+E6+E7+E8) >= 4000
500(C1+C2+C3+C4+C5+C6+C7+C8+C9)+100(G1+G2+G3+G4+G5+G6+G7+G8+G9)+50(W1+W2+W3+W4+W5+W6+W7+W8+W9)+150(E1+E2+E3+E4+E5+E6+E7+E8+E9) >= 4600
C1+C2+C3+C4+C5+C6+C7+C8+C9 <= 5
G1+G2+G3+G4+G5+G6+G7+G8+G9 <= 10
W1+W2+W3+W4+W5+W6+W7+W8+W9 <= 10
E1+E2+E3+E4+E5+E6+E7+E8+E9 <= 4
Ci, Gi, Wi, Ei integer
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