15 01 2024

Pagina 1

Sets plant /'coal','gas','solar'/ t /2020*2060/; Sets t0(t); t0(t) = yes$(ord(t) eq 1); Parameters c_fx(plant) 'unit cost of installing a plant [$/kW]' c_op(plant) 'unit cost of operating a plant [$/kWh]' cf(plant) 'capacity factor of plant [hours equivalent/(hours*yr)]' lifetime(plant) 'lifetime of the plant' delta(plant) 'capital depreciation factor for the plant'; Scalar prtp 'pure rate of time preference' /0.03/; Scalar tstep /1/; *assume all relevant data, BUT the new ones you need to introduce, are loaded here $batinclude data.gms Parameters dmd(t) 'average (yearly) energy demand' rr(t) 'discount factor' ; Variables I(plant,t) investment in plant [kW*yr-1] K(plant,t) capacity of plant [kW] E(plant,t) energy generated by plant [kWh*yr-1] C(plant,t) cost of plant [$*yr-1] OBJ objective variable; Positive variables E,K,C,I; K.l(plant,t) = 1; K.up(plant,t) = 100; I.up(plant,t) = 10; K.fx("gas",t0) = 0.5; K.fx("coal",t0) = 2; K.fx("solar",t0) = 0; Equations eq_stock eq_en eq_dmd eq_cost eq_obj; eq_stock(plant,t+1).. K(plant,t+1) =E= K(plant,t)*(1-delta(plant))**tstep + I(plant,t)*tstep; eq_en(plant,t).. E(plant,t) =L= K(plant,t)*cf(plant)*8760; eq_cost(plant,t).. C(plant,t) =E= c_fx(plant)*I(plant,t)*lifetime(plant)/tstep + E(plant,t)*c_op(plant); eq_dmd(t).. sum(plant,E(plant,t)) =G= dmd(t); eq_obj.. OBJ =E= sum( (plant,t),C(plant,t)*tstep*rr(t)); Model model_all /all/; solve model_all using lp minimizing OBJ; * Post processing Parameter uf(plant,t) 'Capacity factor'; uf(plant,t) = div0(E.l(plant,t),(K.l(plant,t)*8670)); execute_unload 'data_simple_energy.gdx' QUESTIONS Q1 (2pt) : Explain the difference between free variable, state variable and objective variable. Which are the free variable(s) of the problem above? Q2 (2pt): What is the concept and use of aliases in…