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# Copyright (C) 2016 EDF
# All Rights Reserved
# This code is published under the GNU Lesser General Public License (GNU LGPL)
import numpy as np
# Defines a simple gas storage for optimization and simulation
# No constraint on the storage at the end of optimization period (so the storage will be empty)
class OptimizeGasStorageSwitchingCost :
# Constructor
# p_maxLevel size of the storage
# p_injectionRate injection rate per time step
# p_withdrawalRate withdrawal rate between two time steps
# p_injectionCost injection cost
# p_withdrawalCost withdrawal cost
def __init__(self, p_injectionRate, p_withdrawalRate, p_injectionCost, p_withdrawalCost, p_switchCost, p_regime) :
self.m_injectionRate = p_injectionRate
self.m_withdrawalRate = p_withdrawalRate
self.m_injectionCost = p_injectionCost
self.m_withdrawalCost = p_withdrawalCost
self.m_switchCost = p_switchCost
self.m_regime = p_regime
# define the diffusion cone for parallelism
# p_regionByProcessor region (min max) treated by the processor for the different regimes treated
# returns in each dimension the min max values in the stock that can be reached from the grid p_gridByProcessor for each regime
def getCone(self, p_regionByProcessor) :
extrGrid = np.zeros(1)
extrGrid[0][0] = p_regionByProcessor[0][0] - self.m_withdrawalRate
extrGrid[0][1] = p_regionByProcessor[0][1] + self.m_injectionRate
return extrGrid
# get number of regimes
def getNbRegime(self) :
if isinstance(self.m_regime, int):
return self.m_regime
else:
return self.m_regime.get(self.m_simulator.getCurrentStep())
def getNbRegimeReached(self):
if isinstance(self.m_regime, int):
return self.m_regime
else:
return self.m_regime.get(self.m_simulator.getCurrentStep() + self.m_simulator.getStep())
def getNbControl(self):
return self.getNbRegime()
# defines a step in optimization
# p_grid grid at arrival step after command
# p_stock coordinate of the stock point to treat
# p_condEsp conditional expectation operator
# p_phiIn for each regime gives the solution calculated at the previous step ( next time step by Dynamic Programming resolution)
# for each regimes (column) gives the solution for each particle (row)
def stepOptimize(self, p_grid, p_stock, p_condEsp, p_phiIn) :
# number of regime allowed at the beginning of the time step
nbReg = self.getNbRegime()
actuStep= self.m_simulator.getActuStep()
# number of regimes reached to test
nbRegReached = self.getNbRegimeReached()
nbSimul = self.m_simulator.getNbSimul()
solutionAndControl = list(range(2))
solutionAndControl[0] = np.zeros((nbSimul, nbReg))
solutionAndControl[1] = np.zeros((nbSimul, nbReg))
# Spot price
spotPrice = self.m_simulator.fromParticlesToSpot(self.m_simulator.getParticles())
# size of the stock
maxStorage = p_grid.getExtremeValues()[0][1]
# injection
injectionMax = min(maxStorage - p_stock[0], self.m_injectionRate)
# level min of the stock
minStorage = p_grid.getExtremeValues()[0][0]
withdrawalMax = min(p_stock[0] - minStorage, self.m_withdrawalRate)
if (injectionMax < (0. - 1e3 * 2.220446049250313e-16)) & (withdrawalMax < (0. - 1e3 * 2.220446049250313e-16)):
# not an admissible point
solutionAndControl[0].setConstant(-1.e30)
solutionAndControl[1].setConstant(0.)
return solutionAndControl
# Suppose that non injection and no withdrawal
if p_grid.isInside(p_stock):
# create interpolator at current stock point
interpolatorCurrentStock = p_grid.createInterpolator(p_stock)
# cash flow at current stock and previous step
cashSameStock = interpolatorCurrentStock.applyVec(p_phiIn[0])
# conditional expectation at current stock point
condExpSameStock = actuStep * p_condEsp[0].getAllSimulations(interpolatorCurrentStock).squeeze()
cashInjectionStock = []
if (0. < (injectionMax - 1e3 * 2.220446049250313e-16)) & (nbRegReached >= 2):
injectionStock = p_stock + injectionMax
# interpolator for stock level if injection
interpolatorInjectionStock = p_grid.createInterpolator(injectionStock)
# cash flow at previous step at injection level
cashInjectionStock = interpolatorInjectionStock.applyVec(p_phiIn[1]).squeeze()
# conditional expectation at injection stock level
condExpInjectionStock = actuStep * p_condEsp[0].getAllSimulations(interpolatorInjectionStock).squeeze()
cashWithdrawalStock = []
# withdrawal
if (0. < (withdrawalMax - 1e3 * 2.220446049250313e-16)) & (nbRegReached == 3):
withdrawalStock = p_stock - withdrawalMax
# interpolator for stock level if withdrawal
interpolatorWithdrawalStock = p_grid.createInterpolator(withdrawalStock)
# cash flow at previous step at injection level
cashWithdrawalStock = interpolatorWithdrawalStock.applyVec(p_phiIn[2]).squeeze()
# conditional expectation at withdrawal stock level
condExpWithdrawalStock = actuStep * p_condEsp[0].getAllSimulations(interpolatorWithdrawalStock).squeeze()
gainInjection = np.zeros((len(spotPrice), 3))
gainWithdrawal = np.zeros((len(spotPrice), 3))
gainSameStock = np.zeros((len(spotPrice), 3))
# suppose that current regime is 0 (Do Nothing)
gainInjection[:,0] = - injectionMax * (spotPrice + self.m_injectionCost) - self.m_switchCost
gainWithdrawal[:,0] = withdrawalMax * (spotPrice - self.m_withdrawalCost) - self.m_switchCost
# Regime 1) : injection
gainInjection[:,1] = - injectionMax * (spotPrice + self.m_injectionCost)
gainWithdrawal[:,1] = withdrawalMax * (spotPrice - self.m_withdrawalCost) - self.m_switchCost
gainSameStock[:,1] = np.zeros(len(gainSameStock[:,1])) - self.m_switchCost
# Regime 2) : withdrawal
gainInjection[:,2] = - injectionMax * (spotPrice + self.m_injectionCost) - self.m_switchCost
gainWithdrawal[:,2] = withdrawalMax * (spotPrice - self.m_withdrawalCost)
gainSameStock[:,2] = np.zeros(len(gainSameStock[:,2])) - self.m_switchCost
# now arbitrage in each regime
for iReg in range(nbReg):
if ((len(cashInjectionStock) > 0) & (len(cashWithdrawalStock) > 0)):
if nbRegReached == 3:
# do the arbitrage
solutionAndControl[0][:,iReg] = gainSameStock[:,iReg] + np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
espCondMax = condExpSameStock
espCondInjection = gainInjection[:,iReg] + condExpInjectionStock
solutionAndControl[0][:,iReg] = np.where(espCondInjection > espCondMax, gainInjection[:,iReg] + actuStep * cashInjectionStock, solutionAndControl[0][:,iReg])
solutionAndControl[1][:,iReg] = np.where(espCondInjection > espCondMax, injectionMax, solutionAndControl[1][:,iReg])
espCondMax = np.where(espCondInjection > espCondMax, espCondInjection, espCondMax)
espCondWithdrawal = gainWithdrawal[:,iReg] + condExpWithdrawalStock
solutionAndControl[0][:,iReg] = np.where(espCondWithdrawal > espCondMax, gainWithdrawal[:,iReg] + actuStep * cashWithdrawalStock, solutionAndControl[0][:,iReg])
solutionAndControl[1][:,iReg] = np.where(espCondWithdrawal > espCondMax, - withdrawalMax, solutionAndControl[1][:,iReg])
elif nbRegReached == 2:
# do the arbitrage
solutionAndControl[0][:,iReg] = gainSameStock[:,iReg] + np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
espCondMax = condExpSameStock
espCondInjection = gainInjection[:,iReg] + condExpInjectionStock
solutionAndControl[0][:,iReg] = np.where(espCondInjection > espCondMax, gainInjection[:,iReg] + actuStep * cashInjectionStock, solutionAndControl[0][:,iReg])
solutionAndControl[1][:,iReg] = np.where(espCondInjection > espCondMax, injectionMax, solutionAndControl[1][:,iReg])
else:
solutionAndControl[0][:,iReg] = gainSameStock[:,iReg] + np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
elif len(cashWithdrawalStock) > 0:
if len(cashSameStock) > 0:
if nbRegReached == 3:
# do the arbitrage
solutionAndControl[0][:,iReg] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
espCondMax = condExpSameStock - self.m_switchCost
espCondWithdrawal = gainWithdrawal[:,iReg] + condExpWithdrawalStock
solutionAndControl[0][:,iReg] = np.where(espCondWithdrawal > espCondMax, gainWithdrawal[:,iReg] + actuStep * cashWithdrawalStock, solutionAndControl[0][:,iReg])
solutionAndControl[1][:,iReg] = np.where(espCondWithdrawal > espCondMax, - withdrawalMax, solutionAndControl[1][:,iReg])
else:
solutionAndControl[0][:,iReg] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
else:
if nbRegReached == 3:
solutionAndControl[0][:,iReg] = gainWithdrawal[:,iReg] + np.multiply(actuStep, cashWithdrawalStock).transpose()
solutionAndControl[1][:,iReg] = - withdrawalMax
else:
solutionAndControl[0][:,iReg].setConstant(-1.e30)
solutionAndControl[1][:,iReg] = 0.
elif len(cashInjectionStock) > 0:
if len(cashSameStock) > 0:
if nbRegReached >= 2:
# do the arbitrage
solutionAndControl[0][:,iReg] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
espCondMax = condExpSameStock
espCondInjection = gainInjection[:,iReg] + condExpInjectionStock
solutionAndControl[0][:,iReg] = np.where(espCondInjection > espCondMax, gainInjection[:,iReg] + actuStep * cashInjectionStock, solutionAndControl[0][:,iReg])
solutionAndControl[1][:,iReg] = np.where(espCondInjection > espCondMax, injectionMax, solutionAndControl[1][:,iReg])
else:
solutionAndControl[0][:,iReg] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
else:
if nbRegReached >= 2:
solutionAndControl[0][:,iReg] = gainInjection[:,iReg] + actuStep * cashInjectionStock
solutionAndControl[1][:,iReg] = injectionMax
else:
solutionAndControl[0][:,iReg].setConstant(-1.e30)
solutionAndControl[1][:,iReg] = 0.
else:
# only same level
if len(cashSameStock) > 0:
solutionAndControl[0][:,iReg] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,iReg] = 0.
else:
solutionAndControl[0][:,iReg].setConstant(-1.e30)
solutionAndControl[1][:,iReg] = 0.
return solutionAndControl
# defines a step in simulation
# Notice that this implementation is not optimal. In fact no interpolation is necessary for this asset.
# This implementation is for test and example purpose
# p_grid grid at arrival step after command
# p_continuation defines the continuation operator for each regime
# p_state defines the state value (modified)
# p_phiInOut defines the value function (modified)
def stepSimulate(self, p_grid, p_continuation, p_state, p_phiInOut) :
# actualization
actuStep = self.m_simulator.getActuStep()
actu = self.m_simulator.getActu()
# optimal stock attained
ptStockMax = np.zeros(p_state.getPtStock())
# spot price
spotPrice = self.m_simulator.fromOneParticleToSpot(p_state.getStochasticRealization())
# if do nothing
continuationDoNothing = actuStep * p_continuation[0].getValue(p_state.getPtStock(), p_state.getStochasticRealization())
espCondMax = continuationDoNothing
# gain to add at current point
phiAdd = 0
# size of the stock
maxStorage = p_grid.getExtremeValues()[0][1]
# if injection
injectionMax = min(maxStorage - p_state.getPtStock()[0], self.m_injectionRate)
gainInjection = -injectionMax * (spotPrice + self.m_injectionCost)
continuationInjection = actuStep * p_continuation[1].getValue(p_state.getPtStock() + injectionMax, p_state.getStochasticRealization())
espCondInjection = gainInjection + continuationInjection
minStorage = p_grid.getExtremeValues()[0][0]
withdrawalMax = min(p_state.getPtStock()[0] - minStorage, self.m_withdrawalRate)
gainWithdrawal = withdrawalMax * (spotPrice - self.m_withdrawalCost)
continuationWithdrawal = self. m_actu * p_continuation[2].getValue(p_state.getPtStock() - withdrawalMax, p_state.getStochasticRealization())
espCondWithdrawal = gainWithdrawal + continuationWithdrawal
newRegime = 0
if (p_state.getRegime() == 0):
espCondInjection -= self.m_switchCost
espCondWithdrawal -= self.m_switchCost
if (espCondInjection > espCondMax):
espCondMax = espCondInjection
phiAdd = gainInjection - self.m_switchCost
ptStockMax[0] += injectionMax
newRegime = 1
if (espCondWithdrawal > espCondMax):
phiAdd = gainWithdrawal - self.m_switchCost
ptStockMax[0] -= withdrawalMax
newRegime = 2
elif (p_state.getRegime() == 1):
espCondMax -= self.m_switchCost
espCondWithdrawal -= self.m_switchCost
if (espCondInjection > espCondMax):
espCondMax = espCondInjection
phiAdd = gainInjection
ptStockMax[0] += injectionMax
newRegime = 1
else:
phiAdd = -self.m_switchCost
newRegime = 0
if (espCondWithdrawal > espCondMax):
phiAdd = gainWithdrawal - self.m_switchCost
ptStockMax[0] -= withdrawalMax
newRegime = 2
else: # regime withdrawal
espCondMax -= self.m_switchCost
espCondInjection -= self.m_switchCost
if (espCondInjection > espCondMax):
espCondMax = espCondInjection
phiAdd = gainInjection - self.m_switchCost
ptStockMax[0] += injectionMax
newRegime = 1
else:
phiAdd = -self.m_switchCost
newRegime = 0
if (espCondWithdrawal > espCondMax):
phiAdd = gainWithdrawal
ptStockMax[0] -= withdrawalMax
newRegime = 2
# for return
p_state.setPtStock(ptStockMax)
p_state.setRegime(newRegime)
p_phiInOut += phiAdd * actu
# Defines a step in simulation using interpolation in controls
# p_grid grid at arrival step after command
# p_control defines the controls
# p_state defines the state value (modified)
# p_phiInOut defines the value function (modified): size number of functions to follow
def stepSimulateControl(self, p_grid, p_control, p_state, p_phiInOut):
# actualization
actu = self.m_simulator.getActu()
ptStock = p_state.getPtStock()
iReg = p_state.getRegime()
# spot price
spotPrice = self.m_simulator.fromOneParticleToSpot(p_state.getStochasticRealization())
# optimal control
control = p_control[iReg].getValue(p_state.getPtStock(), p_state.getStochasticRealization())
maxStorage = p_grid.getExtremeValues()[0][1]
minStorage = p_grid.getExtremeValues()[0][0]
control = max(min(maxStorage - ptStock[0], control), minStorage - ptStock[0])
if control > 0:
# already injection
p_phiInOut[0] -= control * (spotPrice + self.m_injectionCost) * actu
p_state.setRegime(1)
if iReg != 1:
p_phiInOut[0] -= self.m_switchCost
p_state.setRegime(1)
elif control < 0:
p_phiInOut[0] -= control * (spotPrice - self.m_withdrawalCost) * actu
if iReg != 2:
p_phiInOut[0] -= self.m_switchCost
p_state.setRegime(2)
else:
# do nothing
if iReg != 0:
p_phiInOut[0] -= self.m_switchCost
p_state.setRegime(0)
ptStock[0] += control
p_state.setPtStock(ptStock)
# store the simulator
def setSimulator(self, p_simulator):
self.m_simulator = p_simulator
# get the simulator back
def getSimulator(self):
return self.m_simulator
# get size of the function to follow in simulation
def getSimuFuncSize(self):
return 1
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