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# Copyright (C) 2018 The Regents of the University of California, Michael Ludkovski and Aditya Maheshwari
# All Rights Reserved
# This code is published under the GNU Lesser General Public License (GNU LGPL)
from __future__ import division
import numpy as np
import math
import matplotlib.pyplot as plt
import microGrid.parameters as bv
import time
def penalty(param,inventory):
return ((inventory - param.I0)**2)*0
def finalValue(param,demand,inventory):
if param.rmctype == 'regress now 2D':
nsim = len(demand)
value = np.zeros((nsim,param.H+1))
for q in range(param.H+1):
value[:,q] = penalty(param,inventory)
return value
elif param.rmctype == 'gd':
nsim = len(demand)
gridI = len(inventory)
value = np.zeros((nsim,gridI*(param.H+1)))
for i in range(gridI):
for q in range(param.H+1):
value[:,q*gridI + i] = penalty(param,inventory[i])
return value
def continuationVal(contValObject,x0,i0,q,nextInventory,nextq, type):
if type=='regress now 2D':
return contValObject.getValue([nextq],[x0,nextInventory])
if type=='gd':
return contValObject.getValue([nextInventory, nextq],[x0])
def currentCost(param,currentSt, control, switchCost):
# assuming the cost function is of the type
# c1*d^a + c2*1{st>0} + c3*st*1{st<0}
cost = param.c1*(control**param.a)*param.dt + (param.c2*(currentSt if currentSt>0 else 0) + param.c3*(-currentSt if currentSt<0 else 0))*param.dt
if switchCost == "No":
return cost
else:
return cost + param.K
def calculateCost(param,currentSt, contValObject, x0,i0,q,control,i1,q1,ohc,switchCost="No"):
return currentCost(param,currentSt, control, switchCost) + max(continuationVal(contValObject,x0,i0,q,i1,q1,param.rmctype),0)
# one step optimization
def findOptimalControl(x0, i0, q, contValObject, param):
B_max = param.B_minMax[1]
B_min = param.B_minMax[0]
I_max = param.I_minMax[1]
I_min = param.I_minMax[0]
maxOutputBattery = ((i0 - I_min)/param.dt)
maxInputBattery = - (I_max - i0)/param.dt
maxOutputBattery = (B_max if maxOutputBattery>B_max else maxOutputBattery)
maxInputBattery = (B_min if maxInputBattery<B_min else maxInputBattery)
if param.controlType == "BangBang":
possibleControl = np.zeros((1,2))
possibleControl[:,0] = 0
possibleControl[:,1] = x0*(x0>0) + np.abs(maxInputBattery)
else:
possibleControl = param.discrertize_d
demandExContol = x0 - possibleControl; # nparray of shape (1 rows and 2 columns)
St = np.where((demandExContol<=maxOutputBattery) & (demandExContol>=maxInputBattery),0,demandExContol)
St = np.where((demandExContol>maxOutputBattery),demandExContol - maxOutputBattery,St)
St = np.where((demandExContol<maxInputBattery),demandExContol - maxInputBattery,St)
Bt = demandExContol - St
nextInventory = i0 - Bt*param.dt
nextq = np.ones_like(demandExContol)
nextq[:,0] = 0
contVal = np.zeros_like(demandExContol)
if param.controlType == "BangBang":
contVal[:,0] = continuationVal(contValObject,x0,i0,q,nextInventory[0,0],nextq[0,0], param.rmctype)
contVal[:,1] = continuationVal(contValObject,x0,i0,q,nextInventory[0,1],nextq[0,1], param.rmctype)
else:
for i in range(len(param.discrertize_d[0,:])):
contVal[:,i] = max(continuationVal(contValObject,x0,i0,q,nextInventory[0,i],nextq[0,i], param.rmctype),0)
cost = param.c1*(possibleControl**param.a)*param.dt + param.c2*np.where(St>0, St, 0)*param.dt + param.c3*np.where(St<0, -St, 0)*param.dt + contVal
if q==0:
switchCost = np.zeros_like(demandExContol) + param.K
switchCost[:,0] = 0
cost=cost+switchCost
if param.controlType == "BangBang":
indx = possibleControl[:,1]<0.000001
cost[indx,1]=10**11
indx = np.argmin(cost,1)
return cost[0, indx], possibleControl[0,indx], St[0,indx], nextInventory[0,indx], Bt[0,indx]
def optimization(contValObject, demand, inventory, param):
regime = np.arange(0,param.H+1,1)
lc = len(regime)
nsim = len(demand)
if param.rmctype == 'gd':
gridI = len(inventory)
elif param.rmctype == 'regress now 2D':
gridI = 1
value = np.zeros((nsim,lc*gridI))
policy_d = np.zeros((nsim,lc*gridI))
StOuput = np.zeros((nsim,lc*gridI))
StOuput[:,:]=np.nan
policy_m = np.zeros((nsim,lc*gridI))
policy_m[:,:]=None
# iteration over each sample of residual demand
for i in range(nsim):
# iteration over each regime
for q in regime:
if param.rmctype == 'gd':
# if rmctype is grid-discretization (gd) then iterate over grid levels.
for j in range(gridI):
value[i,q*gridI + j], policy_d[i,q*gridI + j], StOuput[i,q*gridI + j], _, _ = findOptimalControl(demand[i], inventory[j], q, contValObject, param)
elif param.rmctype == 'regress now 2D':
value[i,q], policy_d[i,q], StOuput[i,q], _, _ = findOptimalControl(demand[i], inventory[i], q, contValObject, param)
return value,policy_d, StOuput
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