Optimizing the strategy of a hydro power station in the electricity market.

GAMS
1

I have tried with no sucess to modelate this problem:

OPTIMIZATION MODELING PROJECTS

5 13/09/2017

II Optimizing the strategy of a hydro power station in the electricity market. A utility that owns hydro power stations is willing to optimize its daily strategy in the electricity market for the upcoming month. This is the representation of the system of dams that it owns:

where:

  • I1, I2: Natural Inflows - T1, T2: Hydro power stations - S1, S2: Hydro spillages. - Maximum capacity of R1: 100 GWh - Maximum capacity of R2: 40 GWh - Maximum daily production for T1: 20 GWh - Maximum daily production for T2: 30 GWh - Initial level of R1: 50 GWh - Initial level of R2: 10 GWh - Final desired level of R1: 75 GWh - Final desired level of R2: 10 GWh
    And these are both the daily inflows and prices that they are expecting:

    INFLOWS 1 (MWh)
    INFLOWS 2 (MWh)
    PRICES (€/MWh)
    INFLOWS 1 (MWh)
    INFLOWS 2 (MWh)
    PRICES (€/MWh)
    INFLOWS 1 (MWh)
    INFLOWS 2 (MWh)
    PRICES (€/MWh) d1 6400 1000 50 d11 10100 1900 10 d21 7400 1200 10 d2 5700 900 50 d12 8100 1700 10 d22 7100 1100 70 d3 5400 900 20 d13 12200 1700 40 d23 5600 1000 40 d4 8800 1100 10 d14 21900 2200 50 d24 6100 1100 50 d5 10700 1600 10 d15 18200 2200 80 d25 5200 1100 60 d6 15000 2100 0 d16 12100 1800 90 d26 5400 1100 10 d7 13000 2100 0 d17 9100 1500 50 d27 4600 1000 0 d8 21200 2500 10 d18 8800 1300 20 d28 5200 1000 0 d9 12400 2600 40 d19 7500 1400 30 d29 8800 1200 0 d10 11900 2400 40 d20 7300 1200 40 d30 14300 1400 10


    a) Which should be the optimal daily production pattern that the company should carry out in order to obtain the maximum benefit?
    OPTIMIZATION MODELING PROJECTS

b) How much more money would the company earn if the maximum daily production of the hydro power plant 2 rose in 10 GWh?

c) Due to environmental constraints, the total generating outcome of the hydro power station 2 must be lower or equal to 250 GWh in the whole month. How does the strategy change in that case?

And this is my code for GAMS:

SETS
i natural inflows /I1,I2/
j hydro power stations /T1,T2/
k hydro spillages /S1,S2/
l tanks /R1,R2/
m days /D1,D2,D3,D4,D5,D6,D7,D8,D9,D10,D11,D12,D13,D14,D15,D16,D17,D18,D19,D20,D21,D22,D23,D24,D25,D26,D27,D28,D29,D30/

PARAMETERS
c(l) maximun capacity of tank l
/R1 100000, R2 40000/
a(j) maximun daily production for j
/T1 20000, T2 30000/
b(l) initial level of tank l
/R1 50000, R2 10000/
d(l) desired final desired level of tank l
/R1 75000, R2 10000/
p(m) price of MWh in day m
/D1 50, D2 50, D3 20, D4 10, D5 10, D6 0, D7 0, D8 10, D9 40, D10 40, D11 10, D12 10, D13 40, D14 50, D15 80, D16 90, D17 50, D18 20, D19 30, D20 40, D21 10, D22 70, D23 40, D24 50, D25 60, D26 10, D27 0, D28 0, D29 0, D30 10/

TABLE w(m,i) daily inflow of day m of i
I1 I2
D1 6400 1000
D2 5700 900
D3 5400 900
D4 8800 1100
D5 10700 1600
D6 15000 2100
D7 13000 2100
D8 21200 2500
D9 12400 2600
D10 11900 2400
D11 10100 1900
D12 8100 1700
D13 12200 1700
D14 21900 2200
D15 18200 2200
D16 12100 1800
D17 9100 1500
D18 8800 1300
D19 7500 1400
D20 7300 1200
D21 7400 1200
D22 7100 1100
D23 5600 1000
D24 6100 1100
D25 5200 1100
D26 5400 1100
D27 4600 1000
D28 5200 1000
D29 8800 1200
D30 14300 1400

VARIABLES
VFO value of the objective function: maximize the benefit by carrying out the optimal daily production pattern
X(j,m) MWh produced by the hydro power station j in day m
Y(m) spillages in MWh in S1 in day m
Z(m) spillages in MWh in S2 in day m
E(m,l) level of tank l at beggining of day m
F(m,l) level of tank l at the end of day m
POSITIVE VARIABLES X,Y,Z,E,F

EQUATIONS
OF objective function: maximizing the benefits
RESTRICTION1(m,l) the capacity of the tank l at day m can’t be overpassed
LEV1(m) level of R1 in the end of day m
LEV2(m) level of R2 in the end of day m
CONDITION(m,l) the level of l at the end of day m equals to the level of l at the beggining of day m+1
LEVIN(l) initial level of l
LEVFIN(l) final level of l
PRODMAX1(m) maximun production of T1
PRODMAX2(m) maximun production of T2
;
OF … VFO =E= SUM((j,m),X(j,m)*p(m));
CONDITION(m,l) … E(m+1,l) =E= F(m,l);
LEVIN(l) … E(‘D1’, l) =E= b(l);
LEVFIN(l) … F(‘D30’, l) =E= d(l);
RESTRICTION1(m,l) … E(m,l) =L= c(l);
PRODMAX1(m) … X(‘T1’,m) =L= a(‘T1’);
PRODMAX2(m) … X(‘T2’,m) =L= a(‘T2’);
LEV1(m) … F(m,‘R1’) =E= E(m,‘R1’)+w(m,‘I1’)-X(‘T1’,m)-Y(m);
LEV2(m) … F(m,‘R2’) =E= E(m,‘R2’)+w(m,‘I2’)+X(‘T1’,m)+Y(m)-X(‘T2’,m)-Z(m);
;

MODEL SECTION_A /ALL/

SOLVE SECTION_A USING LP MAXIMIZING VFO


Can anybody please help me?? Thanks soo much :slight_smile: