Problems regarding Pyomo provided math functions - python-3.x

Question

I am trying to solve a maximization problem using Pyomo which has a recursive relationship. I am trying to maximize the revenue from a battery and it involves updating the state of charge of the battery every hour (which is the recursive relationship here). I am using the following code:
import pyomo
import numpy as np
from pyomo.environ import *
import pandas as pd
model = ConcreteModel()
N = 24 #number of hours
lmpdata = np.random.randint(1,10,24) #LMP Data (to be imported from MISO/PJM)
R = 0 #discount
eta_s = 0.99 #self-discharge efficiency
eta_c = 0.95 #round-trip efficiency
gammas_min = 0.1 #fraction of energy capacity to reserve for discharging
gammas_max = 0.05 #fraction of energy capacity to reserve for charging
S_bar = 50 #energy capacity
Q_bar = 50 #energy charge/discharge rating
model.qd = Var(range(N), within = NonNegativeReals) #variables for energy sold at time t
model.qr = Var(range(N), within = NonNegativeReals) #variables for energy purchased at time t
model.obj = Objective(expr = sum((model.qd[i]-model.qr[i])*lmpdata[i]*np.exp(-R*(i+1)) for i in range(N)), sense = maximize) #objective function
model.SOC = np.zeros(N) #state of charge (s(t) in Sandia's Model)
model.SOC[0] = 25 #SOC at hour 0
#recursion relation describing the SOC
def con_rule1(model,i):
model.SOC[i] = eta_s*model.SOC[i-1] + eta_c*model.qr[i-1] - model.qd[i-1]
return (eta_s*model.SOC[i-1] + eta_c*model.qr[i-1] - model.qd[i-1]== model.SOC[i])
#def con_rule1(model,i):
model.con1 = Constraint(range(1,N), rule = con_rule1)
#model.con2 = Constraint(expr = eta_s*SOC[N-1] + eta_c*model.qr[N-1] - model.qd[N-1] == SOC[0]) #SOC relation for the last hour
#SOC boundaries
def con_rule2(model,i):
return (gammas_min*S_bar <= eta_s*model.SOC[i] + eta_c*model.qr[i] - model.qd[i] <= (1-gammas_max)*S_bar)
model.con3 = Constraint(range(N), rule = con_rule2)
#limits the total energy charged over each time step to the energy
#charge limit (derived from the power limit)
#It restricts the throughput based on the power rating
def con_rule3(model,i):
return (0 <= model.qr[i]+model.qd[i] <= Q_bar)
model.con4 = Constraint(range(N),rule = con_rule3)
def pyomo_postprocess(options=None, instance=None, results=None):
model.qd.display()
model.qr.display()
model.pprint()
However, when I try to run the code, I am getting the following error:
Implicit conversion of Pyomo NumericValue type `<class 'pyomo.core.kernel.expr_coopr3._SumExpression'>' to a float is
disabled. This error is often the result of using Pyomo components as
arguments to one of the Python built-in math module functions when
defining expressions. Avoid this error by using Pyomo-provided math
functions.
I could not find any reference to Pyomo's math function in its documentation. It would be great if anyone could help me solve this problem!

Answer 1

Pyomo defines its own set of math module functions for operations like exp, log, sin, etc. If you want to use any of these functions in your Pyomo expressions you should make sure they are the ones provided by Pyomo and not from some other Python package. I think the issue with your model is that you are using np.exp in your Objective function. The Pyomo math functions are automatically imported when you import pyomo.environ so you should be able to replace np.exp with exp to get the Pyomo-defined function.