能源系统的Python GEKKO MINLP优化：如何构建2D阵列的中间体

时间：2019-11-29 10:52:09

标签： python arrays optimization gekko

我目前正在Python GEKKO中实现MINLP优化问题，以确定三代能源系统的最佳运行策略。当我将不同代表天的所有时段的能源需求视为输入数据时，基本上我所有的决策变量，中间物等都是2D数组。 我怀疑2D中间体的声明是我的问题。现在，我使用列表推导来声明2D中间体，但似乎python无法使用这些中间体。此外，错误此稳态IMODE仅允许标量值。发生。

每当我使用GEKKO m.Array函数时，如下所示： e_GT = m.Array(m.Intermediate(E_GT[z][p]/E_max_GT) for z in range(Z) for p in range(P), (Z,P)) 它说，不能调用GEKKO对象m.Intermediate。

如果有人能给我一个提示，我将非常感激。

这是完整的代码：

"""
Created on Fri Nov 22 10:18:33 2019

@author: julia
"""
# __Get GEKKO & numpy___
from gekko import GEKKO
import numpy as np

# ___Initialize model___
m = GEKKO()

# ___Global options_____
m.options.SOLVER = 1                                                            # APOPT is MINLP Solver

# ______Constants_______                                                       
i = m.Const(value=0.05)                                                        
n = m.Const(value=10)                                                          
C_GT = m.Const(value=100000)                                                                         
C_RB = m.Const(value=10000)                                                            
C_HB = m.Const(value=10000)                                                            
C_RS = m.Const(value=10000)                                                           
C_RE = m.Const(value=10000)                                                          
Z = 12                                                                         
P = 24                                                                       
E_min_GT = m.Const(value=1000)                                                 
E_max_GT = m.Const(value=50000)                                                
F_max_GT = m.Const(value=100000)                                               
Q_max_GT = m.Const(value=100000)                                               
a = m.Const(value=1)                                                           
b = m.Const(value=1)                                                           
c = m.Const(value=1)                                                            
d = m.Const(value=1)                                                           
eta_RB = m.Const(value=0.01)                                                   
eta_HB = m.Const(value=0.01)                                                   
eta_RS = m.Const(value=0.01)                                                   
eta_RE = m.Const(value=0.01)                                                    
alpha = m.Const(value=0.01)                                                     

# ______Parameters______
T_z = m.Param([31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31])                
C_p_Gas = m.Param(np.ones([P]))  
C_p_Elec = m.Param(np.ones([P]))
E_d = np.ones([Z,P])
H_d = np.ones([Z,P])
K_d = np.ones([Z,P])

# _______Variables______
E_purch = m.Array(m.Var, (Z,P), lb=0)                                           
E_GT = m.Array(m.Var, (Z,P), lb=0)                                              
F_GT = m.Array(m.Var, (Z,P), lb=0)                                              
Q_GT = m.Array(m.Var, (Z,P), lb=0)                                              
Q_GT_RB = m.Array(m.Var, (Z,P), lb=0)                                          
Q_disp = m.Array(m.Var, (Z,P), lb=0)                                           
Q_HB = m.Array(m.Var, (Z,P), lb=0)                                              
K_RS = m.Array(m.Var, (Z,P), lb=0)                                              
K_RE = m.Array(m.Var, (Z,P), lb=0)                                              
delta_GT = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True)                      
delta_RB = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True)                      
delta_HB = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True)                      
delta_RS = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True)                     
delta_RE = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True)                      

# ____Intermediates_____      
R = m.Intermediate((i*(1+i)**n)/((1+i)**n-1))                                   
e_min_GT = m.Intermediate(E_min_GT/E_max_GT)                                    
e_GT = [m.Intermediate(E_GT[z][p]/E_max_GT) for z in range(Z) for p in range(P)]
f_GT = [m.Intermediate(F_GT[z][p]/F_max_GT) for z in range(Z) for p in range(P)]      
q_GT = [m.Intermediate(Q_GT[z][p]/Q_max_GT) for z in range(Z) for p in range(P)]                                  
Q_RB = [m.Intermediate(eta_RB*Q_GT_RB[z][p]*delta_RB[z][p]) for z in range(Z) for p in range(P)]   
F_HB = [m.Intermediate(eta_HB*Q_HB[z][p]*delta_HB[z][p]) for z in range(Z) for p in range(P)]       
Q_RS = [m.Intermediate(eta_RS*K_RS[z][p]*delta_RS[z][p]) for z in range(Z) for p in range(P)]       
E_RE = [m.Intermediate(eta_RE*K_RE[z][p]*delta_RE[z][p])  for z in range(Z) for p in range(P)]      
F_Gas = [m.Intermediate(F_GT[z][p] + eta_HB*Q_HB[z][p]*delta_HB[z][p]) for z in range(Z) for p in range(P)]                 
Cc = m.Intermediate(R*(C_GT + C_RB + C_HB + C_RS + C_RE))                                           
Cr_z = m.Intermediate((sum(C_p_Gas[p]*F_Gas[z][p] + C_p_Elec[p]*E_purch[z][p]) for p in range(P)) for z in range(Z)) 
Cr = m.Intermediate(sum(Cr_z[z]*T_z[z]) for z in range(Z))                                           

# ______Equations_______                                                
m.Equation(e_min_GT[z][p]*delta_GT[z][p] <= e_GT[z][p] for z in range(Z) for p in range(P))         
m.Equation(e_GT[z][p] <= 1*delta_GT[z][p] for z in range(Z) for p in range(P))                      
m.Equation(f_GT [z][p]== a*delta_GT[z][p] + b*e_GT[z][p] for z in range(Z) for p in range(P))       
m.Equation(q_GT [z][p]== c*delta_GT[z][p] + d*e_GT[z][p] for z in range(Z) for p in range(P))        
m.Equation(E_purch[z][p] + E_GT[z][p] == E_RE[z][p] + E_d[z][p] for z in range(Z) for p in range(P)) 
m.Equation(Q_GT[z][p] == Q_disp[z][p] + Q_GT_RB[z][p] for z in range(Z) for p in range(P))          
m.Equation(Q_RB[z][p] + Q_HB[z][p] == Q_RS[z][p] + H_d[z][p] for z in range(Z) for p in range(P))    
m.Equation(K_RS[z][p] + K_RE[z][p] == K_d[z][p] for z in range(Z) for p in range(P))                 
m.Equation(Q_disp[z][p] <= alpha*Q_GT[z][p] for z in range(Z) for p in range(P))                     

# ______Objective_______
m.Obj(Cc + Cr)

#_____Solve Problem_____
m.solve()

2 个答案:

答案 0 :(得分：3)

2D列表定义需要额外的方括号。这将给出一个具有3行4列的2D列表。

[[p+10*z for p in range(3)] for z in range(4)]
# Result: [[0, 1, 2], [10, 11, 12], [20, 21, 22], [30, 31, 32]]

如果省略内括号，则为一维长度为12的列表。

[p+10*z for p in range(3) for z in range(4)]
# Result: [0, 10, 20, 30, 1, 11, 21, 31, 2, 12, 22, 32]

当列表的每个元素都是Gekko Intermediate时，它也适用。

[[m.Intermediate(p+10*z) for p in range(3)] for z in range(4)]

答案 1 :(得分：2)

为诊断问题，我在solve命令之前添加了一个调用以打开运行文件夹。

#_____Solve Problem_____
m.open_folder()
m.solve()

我使用文本编辑器打开了gk_model0.apm模型文件，以查看模型的文本版本。在底部显示出最后两个中间体和9个方程式存在问题。

    i2327=<generator object <genexpr> at 0x0E51BC30>
    i2328=<generator object <genexpr> at 0x0E51BC30>
End Intermediates
Equations
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    <generator object <genexpr> at 0x0E51BC30>
    minimize (i2326+i2328)
End Equations

End Model

当.value或Param的{​​{1}}属性是列表或numpy数组而不是标量值时，会发生这种情况。

Var

还有其他一些问题，例如

  • # ______Parameters______ #T_z = m.Param([31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]) T_z = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31] 被引用为列表的元素，而不是第一个方程式中的标量值
  • 缺少中间列表中的方括号以使列表2D如e_min_GT
  • 与[[2 for p in range(P)] for z in range(Z)]而不是for z in range(Z)] for p in range(P)]的尺寸不匹配
  • 为了获得更高的效率，请使用for p in range(P)] for z in range(Z)]代替m.sum

我也做了其他一些更改。差异程序应显示它们。

sum

问题通过求解器时间""" Created on Fri Nov 22 10:18:33 2019 @author: julia """ # __Get GEKKO & numpy___ from gekko import GEKKO import numpy as np # ___Initialize model___ m = GEKKO() # ___Global options_____ m.options.SOLVER = 1 # APOPT is MINLP Solver # ______Constants_______ i = m.Const(value=0.05) n = m.Const(value=10) C_GT = m.Const(value=100000) C_RB = m.Const(value=10000) C_HB = m.Const(value=10000) C_RS = m.Const(value=10000) C_RE = m.Const(value=10000) Z = 12 P = 24 E_min_GT = m.Const(value=1000) E_max_GT = m.Const(value=50000) F_max_GT = m.Const(value=100000) Q_max_GT = m.Const(value=100000) a = m.Const(value=1) b = m.Const(value=1) c = m.Const(value=1) d = m.Const(value=1) eta_RB = m.Const(value=0.01) eta_HB = m.Const(value=0.01) eta_RS = m.Const(value=0.01) eta_RE = m.Const(value=0.01) alpha = m.Const(value=0.01) # ______Parameters______ T_z = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31] C_p_Gas = np.ones(P) C_p_Elec = np.ones(P) E_d = np.ones([Z,P]) H_d = np.ones([Z,P]) K_d = np.ones([Z,P]) # _______Variables______ E_purch = m.Array(m.Var, (Z,P), lb=0) E_GT = m.Array(m.Var, (Z,P), lb=0) F_GT = m.Array(m.Var, (Z,P), lb=0) Q_GT = m.Array(m.Var, (Z,P), lb=0) Q_GT_RB = m.Array(m.Var, (Z,P), lb=0) Q_disp = m.Array(m.Var, (Z,P), lb=0) Q_HB = m.Array(m.Var, (Z,P), lb=0) K_RS = m.Array(m.Var, (Z,P), lb=0) K_RE = m.Array(m.Var, (Z,P), lb=0) delta_GT = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True) delta_RB = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True) delta_HB = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True) delta_RS = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True) delta_RE = m.Array(m.Var, (Z,P), lb=0, ub=1, integer=True) # ____Intermediates_____ R = m.Intermediate((i*(1+i)**n)/((1+i)**n-1)) e_min_GT = m.Intermediate(E_min_GT/E_max_GT) e_GT = [[m.Intermediate(E_GT[z][p]/E_max_GT) for p in range(P)] for z in range(Z)] f_GT = [[m.Intermediate(F_GT[z][p]/F_max_GT) for p in range(P)] for z in range(Z)] q_GT = [[m.Intermediate(Q_GT[z][p]/Q_max_GT) for p in range(P)] for z in range(Z)] Q_RB = [[m.Intermediate(eta_RB*Q_GT_RB[z][p]*delta_RB[z][p]) for p in range(P)] for z in range(Z)] F_HB = [[m.Intermediate(eta_HB*Q_HB[z][p]*delta_HB[z][p]) for p in range(P)] for z in range(Z)] Q_RS = [[m.Intermediate(eta_RS*K_RS[z][p]*delta_RS[z][p]) for p in range(P)] for z in range(Z)] E_RE = [[m.Intermediate(eta_RE*K_RE[z][p]*delta_RE[z][p]) for p in range(P)] for z in range(Z)] F_Gas = [[m.Intermediate(F_GT[z][p] + eta_HB*Q_HB[z][p]*delta_HB[z][p]) for p in range(P)] for z in range(Z)] Cc = m.Intermediate(R*(C_GT + C_RB + C_HB + C_RS + C_RE)) Cr_z = [m.Intermediate(m.sum([C_p_Gas[p]*F_Gas[z][p] + C_p_Elec[p]*E_purch[z][p] for p in range(P)])) for z in range(Z)] Cr = m.Intermediate(m.sum([Cr_z[z]*T_z[z] for z in range(Z)])) # ______Equations_______ m.Equation([e_min_GT*delta_GT[z][p] <= e_GT[z][p] for z in range(Z) for p in range(P)]) m.Equation([e_GT[z][p] <= 1*delta_GT[z][p] for z in range(Z) for p in range(P)]) m.Equation([f_GT [z][p]== a*delta_GT[z][p] + b*e_GT[z][p] for z in range(Z) for p in range(P)]) m.Equation([q_GT [z][p]== c*delta_GT[z][p] + d*e_GT[z][p] for z in range(Z) for p in range(P)]) m.Equation([E_purch[z][p] + E_GT[z][p] == E_RE[z][p] + E_d[z][p] for z in range(Z) for p in range(P)]) m.Equation([Q_GT[z][p] == Q_disp[z][p] + Q_GT_RB[z][p] for z in range(Z) for p in range(P)]) m.Equation([Q_RB[z][p] + Q_HB[z][p] == Q_RS[z][p] + H_d[z][p] for z in range(Z) for p in range(P)]) m.Equation([K_RS[z][p] + K_RE[z][p] == K_d[z][p] for z in range(Z) for p in range(P)]) m.Equation([Q_disp[z][p] <= alpha*Q_GT[z][p] for z in range(Z) for p in range(P)]) # ______Objective_______ m.Obj(Cc + Cr) #_____Solve Problem_____ #m.open_folder() m.solve() 解决。

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