How to fix "Solution Not Found" Error in Gekko Optimization with rolling principle

Question

My program is optimizing the charging and decharging of a home battery to minimize the cost of electricity at the end of the year. In this case there also is a PV, which means that sometimes you're injecting electricity into the grid and receive money. The electricity usage of homes is measured each 15 minutes, so I have 96 measurement point in 1 day. I want to optimilize the charging and decharging of the battery for 2 days, so that day 1 takes the usage of day 2 into account. I wrote a controller that reads the data and gives each time the input values for 2 days to the optimization. With a rolling principle, it goes to the next 2 days and so on. Below you can see the code from my controller.

from gekko import GEKKO
from simulationModel2_2d_1 import getSimulation2
from exportModel2 import exportToExcelModel2
import numpy as np
#import matplotlib.pyplot as plt
import pandas as pd
import time
import math

# ------------------------ Import and read input data ------------------------

file = r'Data Sim 2.xlsx'

data = pd.read_excel(file, sheet_name='Input', na_values='NaN')

dataRead = pd.DataFrame(data, columns= ['Timestep','Verbruik woning (kWh)','Netto afname (kWh)','Prijs afname (€/kWh)',
                                            'Prijs injectie (€/kWh)','Capaciteit batterij (kW)',
                                            'Capaciteit batterij (kWh)','Rendement (%)',
                                            'Verbruikersprofiel','Capaciteit PV (kWp)','Aantal dagen'])

timestep = dataRead['Timestep'].to_numpy()                                 
usage_home = dataRead['Verbruik woning (kWh)'].to_numpy()
net_offtake = dataRead['Netto afname (kWh)'].to_numpy()
price_offtake = dataRead['Prijs afname (€/kWh)'].to_numpy()
price_injection = dataRead['Prijs injectie (€/kWh)'].to_numpy()
cap_batt_kW = dataRead['Capaciteit batterij (kW)'].iloc[0]              
cap_batt_kWh = dataRead['Capaciteit batterij (kWh)'].iloc[0]
efficiency = dataRead['Rendement (%)'].iloc[0]
usersprofile = dataRead['Verbruikersprofiel'].iloc[0]
days = dataRead['Aantal dagen'].iloc[0]
pv = dataRead['Capaciteit PV (kWp)'].iloc[0]

# ------------- Optimization model & Rolling principle (2 days) --------------

# Initialise model
m = GEKKO()

# Output data
ts = []
charging = []                       # Amount to charge/decharge batterij
e_batt = []                         # Amount of energy in the battery
usage_net = []                      # Usage after home, battery and pv
p_paid = []                         # Price paid for energy of 15min

# Energy in battery to pass
energy = 0

# Iterate each day for one year
for d in range(int(days)-1):
    d1_timestep = []
    d1_net_offtake = []
    d1_price_offtake = []
    d1_price_injection = []
    d2_timestep = []
    d2_net_offtake = []
    d2_price_offtake = []
    d2_price_injection = []
    
    # Iterate timesteps
    for i in range(96):
        d1_timestep.append(timestep[d*96+i])
        d2_timestep.append(timestep[d*96+i+96])
        
        d1_net_offtake.append(net_offtake[d*96+i])
        d2_net_offtake.append(net_offtake[d*96+i+96])
        
        d1_price_offtake.append(price_offtake[d*96+i])
        d2_price_offtake.append(price_offtake[d*96+i+96])
        
        d1_price_injection.append(price_injection[d*96+i])
        d2_price_injection.append(price_injection[d*96+i+96])
    
    # Input data simulation of 2 days
    ts_temp = np.concatenate((d1_timestep, d2_timestep))
    net_offtake_temp = np.concatenate((d1_net_offtake, d2_net_offtake))
    price_offtake_temp = np.concatenate((d1_price_offtake, d2_price_offtake))
    price_injection_temp = np.concatenate((d1_price_injection, d2_price_injection))
    if(d == 7):
        print(ts_temp)
        print(energy)
    # Simulatie uitvoeren
    charging_temp, e_batt_temp, usage_net_temp, p_paid_temp, energy_temp = getSimulation2(ts_temp, net_offtake_temp, price_offtake_temp, price_injection_temp,                                                                                     cap_batt_kW, cap_batt_kWh, efficiency, energy, pv)
    
    # Take over output first day, unless last 2 days
    energy = energy_temp
    if(d == (days-2)):
        for t in range(1,len(ts_temp)):
            ts.append(ts_temp[t])
            charging.append(charging_temp[t])
            e_batt.append(e_batt_temp[t])
            usage_net.append(usage_net_temp[t])
            p_paid.append(p_paid_temp[t])
    elif(d == 0):
        for t in range(int(len(ts_temp)/2)+1):
            ts.append(ts_temp[t])
            charging.append(charging_temp[t])
            e_batt.append(e_batt_temp[t])
            usage_net.append(usage_net_temp[t])
            p_paid.append(p_paid_temp[t])
    else:
        for t in range(1,int(len(ts_temp)/2)+1):
            ts.append(ts_temp[t])
            charging.append(charging_temp[t])
            e_batt.append(e_batt_temp[t])
            usage_net.append(usage_net_temp[t])
            p_paid.append(p_paid_temp[t])
            
    print('Simulation day '+str(d+1)+' complete.')
    
# ------------------------ Export output data to Excel -----------------------

a = exportToExcelModel2(ts, usage_home, net_offtake, price_offtake, price_injection, charging, e_batt, usage_net, p_paid, cap_batt_kW, cap_batt_kWh, efficiency, usersprofile, pv)
print(a)

The optimization with Gekko happens in the following code:

from gekko import GEKKO

def getSimulation2(timestep, net_offtake, price_offtake, price_injection, 
                   cap_batt_kW, cap_batt_kWh, efficiency, start_energy, pv):
    
    # ---------------------------- Optimization model ----------------------------
       
    # Initialise model
    m = GEKKO(remote = False)
    
    # Global options
    m.options.SOLVER = 1
    m.options.IMODE  = 6
    
    # Constants
    speed_charging = cap_batt_kW/4
    m.time = timestep
        
    max_cap_batt = m.Const(value = cap_batt_kWh)
    min_cap_batt = m.Const(value = 0)
    max_charge = m.Const(value = speed_charging)                                    # max battery can charge in 15min
    max_decharge = m.Const(value = -speed_charging)                                 # max battery can decharge in 15min
    
    # Parameters
    usage_home = m.Param(net_offtake)
    price_offtake = m.Param(price_offtake)
    price_injection = m.Param(price_injection)
    
    # Variables
    e_batt = m.Var(value=start_energy, lb = min_cap_batt, ub = max_cap_batt)  # energy in battery
    price_paid = m.Var()                                              # price paid each 15min
    charging = m.Var(lb = max_decharge, ub = max_charge)              # amount charge/decharge each 15min
    usage_net = m.Var(lb=min_cap_batt)
    
    # Equations
    m.Equation(e_batt==(m.integral(charging)+start_energy)*efficiency)
    m.Equation(-charging <= e_batt)
    m.Equation(usage_net==usage_home + charging)
    price = m.Intermediate(m.if2(usage_net*1e6, price_injection, price_offtake))
    price_paid = m.Intermediate(usage_net * price / 100)
    
    # Objective 
    m.Minimize(price_paid)
    
    # Solve problem
    m.options.COLDSTART=2
    m.solve()
    
    m.options.TIME_SHIFT=0
    m.options.COLDSTART=0
    m.solve()
          
    # Energy to pass
    energy_left = e_batt[95]
    
    #m.cleanup()
    
    return charging, e_batt, usage_net, price_paid, energy_left

The data you need for input can be found in this Excel document: https://docs.google.com/spreadsheets/d/1S40Ut9-eN_PrftPCNPoWl8WDDQtu54f0/edit?usp=sharing&ouid=104786612700360067470&rtpof=true&sd=true

With this code, it always ends at day 17 with the "Solution Not Found" Error. I already tried extending the default iteration limit to 500 but it didn't work. I also tried with other solvers but also no improvement. By presolving with COLDSTART it already reached day 17, without this it ends at day 8.

I solved the days were my optimization ends individually and then the solution was always found immediately with the same code. Someone who can explain this to me and maybe find a solution? Thanks in advance!

Answer 1

This is kind of big to troubleshoot, but here are some general ideas that might help. This assumes, as you said, that the model solves fine for day 1-2, and day 3-4, and day 5-6, etc. And that those results pass inspection (aka the basic model is working as you say).

Then something is (obviously) amiss around day 17. Some things to look at and try:

• Start the model at day 16-17, see if it works in isolation
• gather your results as you go and do a time series plot of the key variables, maybe one of them is on an obvious bad trend towards a limit causing an infeasibility... Perhaps the e_batt variable is slowly declining because not enough PV energy is available and hits minimum on Day 17
• Radically change the upper/lower bounds on your variables to test them to see if they might be involved in the infeasibility (assuming there is one)
• Make a different (fake) dataset where the solution is assured and kind of obvious... all constants or a pattern that you know will produce some known result and test the model outputs against it.