Energy optimization with pulp

[MartinRK80]

I'm trying to create my first LP simulation but I have some problem with it.

This is my code:

import pulp

# Define the optimization problem  
prob = pulp.LpProblem("Energy_Cost_Minimization", pulp.LpMinimize)  

# Time horizon
T = 24 

# Battery parameters
B_max = 10    # Maximum battery capacity
B_init = 0    # Initial battery level 

# Grid energy cost per unit for each hour  
grid_cost = [0.15, 0.15, 0.14, 0.13, 0.12, 0.12, 0.12, 0.12, 0.14, 0.16,  
             0.18, 0.20, 0.20, 0.20, 0.18, 0.16, 0.14, 0.18, 0.20, 0.20,  
             0.20, 0.18, 0.16, 0.15]  

# Renewable energy supply for each hour 
S = [1, 1, 0.5, 0.5, 1, 2, 3, 4, 5, 5, 5, 4, 4, 3, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1]  

# Predicted energy demand for each hour
#D = [1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 7, 7, 6, 6, 5, 5, 5, 6, 7, 7, 6, 4, 3, 2]  
D = [0.5, 0.5, 0.5, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 3.5, 3.5, 3, 3, 2.5, 2.5,  
     2.5, 3, 3.5, 3.5, 3, 2, 1.5, 1]
# Create decision variables  
G = pulp.LpVariable.dicts("Grid Energy", range(T), lowBound=0)  
B = pulp.LpVariable.dicts("Battery Level", range(T+1), lowBound=0, upBound=B_max)
Surplus = pulp.LpVariable.dicts("Renewable Surplus", range(T), lowBound=0)

# Objective function       
prob += pulp.lpSum([grid_cost[t] * G[t] for t in range(T)])  

# Constraints
for t in range(T):
    
    if t > 0:
        # Battery can only charge from renewable surplus
        #Surplus[t] = max(0, S[t] - D[t])
        prob += Surplus[t] <= S[t] - D[t] # Calculate renewable surplus
        prob += B[t] <= B[t-1] + Surplus[t-1] # Battery charges from surplus
    
    # Meet demand from renewables, battery and grid 
    prob += D[t] <= S[t] + B[t] + G[t] 
    
    # Battery initialization
    if t == 0: 
        prob += B[t] == B_init # Start battery empty
        
# Solve optimization        
prob.solve()    

# Print results
for t in range(T):
    print(f"Hour {t}: Grid Energy = {G[t].varValue} kWh, Battery Level = {B[t].varValue} kWh, Power Consumption = {D[t]} kWh, Renewable Energy Supply = {S[t]} kWh")

This is the result in colab:

Output:
Hour 0: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 0.5 kWh, Renewable Energy Supply = 1 kWh
Hour 1: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 0.5 kWh, Renewable Energy Supply = 1 kWh
Hour 2: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 0.5 kWh, Renewable Energy Supply = 0.5 kWh
Hour 3: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 0.5 kWh, Renewable Energy Supply = 0.5 kWh
Hour 4: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 1 kWh, Renewable Energy Supply = 1 kWh
Hour 5: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 1.5 kWh, Renewable Energy Supply = 2 kWh
Hour 6: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 2 kWh, Renewable Energy Supply = 3 kWh
Hour 7: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 2.5 kWh, Renewable Energy Supply = 4 kWh
Hour 8: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3 kWh, Renewable Energy Supply = 5 kWh
Hour 9: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3.5 kWh, Renewable Energy Supply = 5 kWh
Hour 10: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3.5 kWh, Renewable Energy Supply = 5 kWh
Hour 11: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3.5 kWh, Renewable Energy Supply = 4 kWh
Hour 12: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3 kWh, Renewable Energy Supply = 4 kWh
Hour 13: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3 kWh, Renewable Energy Supply = 3 kWh
Hour 14: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 2.5 kWh, Renewable Energy Supply = 2 kWh
Hour 15: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 2.5 kWh, Renewable Energy Supply = 3 kWh
Hour 16: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 2.5 kWh, Renewable Energy Supply = 4 kWh
Hour 17: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3 kWh, Renewable Energy Supply = 5 kWh
Hour 18: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3.5 kWh, Renewable Energy Supply = 5 kWh
Hour 19: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3.5 kWh, Renewable Energy Supply = 4 kWh
Hour 20: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 3 kWh, Renewable Energy Supply = 3 kWh
Hour 21: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 2 kWh, Renewable Energy Supply = 2 kWh
Hour 22: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 1.5 kWh, Renewable Energy Supply = 1 kWh
Hour 23: Grid Energy = 0.0 kWh, Battery Level = 0.0 kWh, Power Consumption = 1 kWh, Renewable Energy Supply = 1 kWh

Grid Energy should be positive when renewable energy and battery aren't enough but it is 0.0 at all hours. Also Battery level should charge only if there is a surplus of renewable energy.