how to create a simple capacity expansion model while maximizing the revenue using PYOMO?

Question

I have create a capacity expansion model using PYOMO, where there are 2 main generators gen1 and gen2 and one backup generator lost_load. The logic is pretty simple, gen1 and gen2 will run to fulfill the demand profile and they will get the money for that and there is some negative cost associated with gen1 and gen2 capacity. Here is the code:

import datetime
import pandas as pd
import numpy as np
from pyomo.environ import *


model = ConcreteModel()
np.random.seed(24)
load_profile = np.random.randint(90, 120, 24)
model.m_index = Set(initialize=list(range(len(load_profile))))

model.grid = Var(model.m_index, domain=NonNegativeReals)

#  Gen1 variable
model.gen1_cap = Var(domain=NonNegativeReals)
model.gen1_use = Var(model.m_index, domain=NonNegativeReals)

#  Gen2 variables
model.gen2_cap = Var(domain=NonNegativeReals)
model.gen2_use = Var(model.m_index, domain=NonNegativeReals)

# Load profile
model.load_profile = Param(model.m_index, initialize=dict(zip(model.m_index, load_profile)))

model.lost_load = Var(model.m_index, domain=NonNegativeReals)

# Objective function
def revenue(model):
    total_revenue = sum(
        model.gen1_use[m] * 5.2 +
        model.gen2_use[m] * 6.1 +
        model.lost_load[m] * -100
        for m in model.m_index)

    total_fixed_cost = model.gen1_cap * -45 + model.gen2_cap * -50

    total_cost = total_revenue + total_fixed_cost
    return total_cost


model.obj = Objective(rule=revenue, sense=maximize)

# When i=0
def energy_balance1(model, m):
    return model.grid[m] <= model.gen1_use[m] + model.gen2_use[m] + model.lost_load[m]


model.energy_balance1 = Constraint(model.m_index, rule=energy_balance1)


def grid_limit(model, m):
    return model.grid[m] == model.load_profile[m]


model.grid_limit = Constraint(model.m_index, rule=grid_limit)


def max_gen1(model, m):
    eq = model.gen1_use[m] <= model.gen1_cap
    return eq


model.max_gen1 = Constraint(model.m_index, rule=max_gen1)


def max_gen2(model, m):
    eq = model.gen2_use[m] <= model.gen2_cap
    return eq


model.max_gen2 = Constraint(model.m_index, rule=max_gen2)


Solver = SolverFactory('gurobi')
Solver.options['LogFile'] = "gurobiLog"
# Solver.options['MIPGap'] = 0.50
print('\nConnecting to Gurobi Server...')
results = Solver.solve(model)

if (results.solver.status == SolverStatus.ok):
    if (results.solver.termination_condition == TerminationCondition.optimal):
        print("\n\n***Optimal solution found***")
        print('obj returned:', round(value(model.obj), 2))
    else:
        print("\n\n***No optimal solution found***")
        if (results.solver.termination_condition == TerminationCondition.infeasible):
            print("Infeasible solution")
            exit()
else:
    print("\n\n***Solver terminated abnormally***")
    exit()

grid_use = []
gen1 = []
gen2 = []
lost_load = []
load = []

for i in range(len(load_profile)):
    grid_use.append(value(model.grid[i]))
    gen1.append(value(model.gen1_use[i]))
    gen2.append(value(model.gen2_use[i]))
    lost_load.append(value(model.lost_load[i]))
    load.append(value(model.load_profile[i]))

print('gen1 capacity: ', value(model.gen1_cap))
print('gen2 capacity: ', value(model.gen2_cap))

pd.DataFrame({
    'Grid': grid_use,
    'Gen1': gen1,
    'Gen2': gen2,
    'Shortfall': lost_load,
    'Load': load
}).to_excel('capacity expansion.xlsx')

This model will work if :

def energy_balance1(model, m):
    return model.grid[m] == model.gen1_use[m] + model.gen2_use[m] + model.lost_load[m]


model.energy_balance1 = Constraint(model.m_index, rule=energy_balance1)

But if I set it to (<=) greater than equal to, it gives me an infeasible error. I want this condition because in actuality I want gen1 and gen2 to run at 100% capacity at all 24 instances. After all, in the objective function, we can see the positive cost associated with gen1_use and gen2_use. So to maximize the revenue they should run at 100% capacity even if the load profile is fulfilled. Here is the output I am getting:

optimal gen1 capacity: 9MW
optimal gen2 capacity: 108MW

Although I want the dispatch something like this :

Answer 1

Try something like this to get started. I avoided making capacity a variable by including several distinct generator choices, which seems very reasonable.

This also incorporates a binary "use" variable, which I think you need from the described problem.

CODE:

import pyomo.environ as pyo

demand = [100, 200, 50, 22, 300]
solar_wind = [20, 100, 100, 0, 100]

net_demand = [d - s for (d, s) in zip(demand, solar_wind)]
print(net_demand)


# generator options...
gen_capacity = {'gen1': 25, 'gen2': 25, 'gen3': 50, 'gen4': 100}
running_cost = {'gen1': 12, 'gen2': 12, 'gen3': 30, 'gen4': 50}
shortage_cost = 100

m = pyo.ConcreteModel()

### SETS
m.T = pyo.Set(initialize=range(len(demand)))     # time periods
m.G = pyo.Set(initialize=gen_capacity.keys())    # generators

### VARS
m.install = pyo.Var(m.G, domain=pyo.Binary)
m.use = pyo.Var(m.G, m.T, domain=pyo.Binary)
m.shortage = pyo.Var(m.T, domain=pyo.NonNegativeReals)

### PARAMS
m.use_cost = pyo.Param(m.G, initialize=running_cost)
m.capacity = pyo.Param(m.G, initialize=gen_capacity)

### OBJ
m.cost = pyo.Objective(expr=sum(m.use[g, t] * m.use_cost[g] for g in m.G for t in m.T) +
                       sum(m.shortage[t] * shortage_cost for t in m.T),
                       sense=pyo.minimize)

### CONSTRAINTS

def demand(m, t):
    return sum(m.use[g, t] * m.capacity[g] for g in m.G) + m.shortage[t] >= net_demand[t]
m.C1 = pyo.Constraint(m.T, rule=demand, doc='meet demand')

def use_if_installed(m, g, t):
    return m.use[g, t] <= m.install[g]
m.C2 = pyo.Constraint(m.G, m.T, rule=use_if_installed, doc='can only use if installed')

m.C3 = pyo.Constraint(expr=sum(m.install[g] for g in m.G) <= 2, doc='install at most 2 gens')

solver = pyo.SolverFactory('cbc')
result = solver.solve(m)
print(result)

m.display()

Output (a bit long)

[80, 100, -50, 22, 200]

Problem: 
- Name: unknown
  Lower bound: 5210.0
  Upper bound: 5210.0
  Number of objectives: 1
  Number of constraints: 25
  Number of variables: 28
  Number of binary variables: 24
  Number of integer variables: 24
  Number of nonzeros: 24
  Sense: minimize
Solver: 
- Status: ok
  User time: -1.0
  System time: 0.0
  Wallclock time: 0.0
  Termination condition: optimal
  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.
  Statistics: 
    Branch and bound: 
      Number of bounded subproblems: 0
      Number of created subproblems: 0
    Black box: 
      Number of iterations: 0
  Error rc: 0
  Time: 0.012147188186645508
Solution: 
- number of solutions: 0
  number of solutions displayed: 0

Model unknown

  Variables:
    install : Size=4, Index=G
        Key  : Lower : Value : Upper : Fixed : Stale : Domain
        gen1 :     0 :   0.0 :     1 : False : False : Binary
        gen2 :     0 :   0.0 :     1 : False : False : Binary
        gen3 :     0 :   1.0 :     1 : False : False : Binary
        gen4 :     0 :   1.0 :     1 : False : False : Binary
    use : Size=20, Index=use_index
        Key         : Lower : Value : Upper : Fixed : Stale : Domain
        ('gen1', 0) :     0 :   0.0 :     1 : False : False : Binary
        ('gen1', 1) :     0 :   0.0 :     1 : False : False : Binary
        ('gen1', 2) :     0 :   0.0 :     1 : False : False : Binary
        ('gen1', 3) :     0 :   0.0 :     1 : False : False : Binary
        ('gen1', 4) :     0 :   0.0 :     1 : False : False : Binary
        ('gen2', 0) :     0 :   0.0 :     1 : False : False : Binary
        ('gen2', 1) :     0 :   0.0 :     1 : False : False : Binary
        ('gen2', 2) :     0 :   0.0 :     1 : False : False : Binary
        ('gen2', 3) :     0 :   0.0 :     1 : False : False : Binary
        ('gen2', 4) :     0 :   0.0 :     1 : False : False : Binary
        ('gen3', 0) :     0 :   0.0 :     1 : False : False : Binary
        ('gen3', 1) :     0 :   0.0 :     1 : False : False : Binary
        ('gen3', 2) :     0 :   0.0 :     1 : False : False : Binary
        ('gen3', 3) :     0 :   1.0 :     1 : False : False : Binary
        ('gen3', 4) :     0 :   1.0 :     1 : False : False : Binary
        ('gen4', 0) :     0 :   1.0 :     1 : False : False : Binary
        ('gen4', 1) :     0 :   1.0 :     1 : False : False : Binary
        ('gen4', 2) :     0 :   0.0 :     1 : False : False : Binary
        ('gen4', 3) :     0 :   0.0 :     1 : False : False : Binary
        ('gen4', 4) :     0 :   1.0 :     1 : False : False : Binary
    shortage : Size=5, Index=T
        Key : Lower : Value : Upper : Fixed : Stale : Domain
          0 :     0 :   0.0 :  None : False : False : NonNegativeReals
          1 :     0 :   0.0 :  None : False : False : NonNegativeReals
          2 :     0 :   0.0 :  None : False : False : NonNegativeReals
          3 :     0 :   0.0 :  None : False : False : NonNegativeReals
          4 :     0 :  50.0 :  None : False : False : NonNegativeReals

  Objectives:
    cost : Size=1, Index=None, Active=True
        Key  : Active : Value
        None :   True : 5210.0

  Constraints:
    C1 : Size=5
        Key : Lower : Body  : Upper
          0 :  80.0 : 100.0 :  None
          1 : 100.0 : 100.0 :  None
          2 : -50.0 :   0.0 :  None
          3 :  22.0 :  50.0 :  None
          4 : 200.0 : 200.0 :  None
    C2 : Size=20
        Key         : Lower : Body : Upper
        ('gen1', 0) :  None :  0.0 :   0.0
        ('gen1', 1) :  None :  0.0 :   0.0
        ('gen1', 2) :  None :  0.0 :   0.0
        ('gen1', 3) :  None :  0.0 :   0.0
        ('gen1', 4) :  None :  0.0 :   0.0
        ('gen2', 0) :  None :  0.0 :   0.0
        ('gen2', 1) :  None :  0.0 :   0.0
        ('gen2', 2) :  None :  0.0 :   0.0
        ('gen2', 3) :  None :  0.0 :   0.0
        ('gen2', 4) :  None :  0.0 :   0.0
        ('gen3', 0) :  None : -1.0 :   0.0
        ('gen3', 1) :  None : -1.0 :   0.0
        ('gen3', 2) :  None : -1.0 :   0.0
        ('gen3', 3) :  None :  0.0 :   0.0
        ('gen3', 4) :  None :  0.0 :   0.0
        ('gen4', 0) :  None :  0.0 :   0.0
        ('gen4', 1) :  None :  0.0 :   0.0
        ('gen4', 2) :  None : -1.0 :   0.0
        ('gen4', 3) :  None : -1.0 :   0.0
        ('gen4', 4) :  None :  0.0 :   0.0
    C3 : Size=1
        Key  : Lower : Body : Upper
        None :  None :  2.0 :   2.0