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Copy pathPartition_Univariate.py
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Copy pathPartition_Univariate.py
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2153 lines (2047 loc) · 99.2 KB
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"""
Written by Alex Zolan
Univariate Paritioning Model (U)
This module contains a collection of methods used to build and solve instances
of a Remote Microgrid Optimization Model, which we refer to as Model (U) in the
paper. This model uses McCormick sub-envelopes using a univariate partitioning
scheme to approximate bilinear terms for the product of a battery's current and
its state of charge.
Note that we use a separate module, InputReader, for the
purpose of reading inputs.
"""
#import DieselGenerator, PVArray, Battery
import multiprocessing
import scipy
import InputReader
import cplex
import time
#update working directory to current directory.
import os
#setting one global variable
local = True
def FractionOfSolar(tech,start_period,end_period):
return scipy.sum([tech.CalculatePowerAvailable(t)
for t in range(start_period-1,end_period)]) / scipy.sum([
tech.CalculatePowerAvailable(t)
for t in range(len(tech.GetPVAvailability())) ])
def FractionOfDemand(loads,start_period,end_period):
return sum(loads[start_period-1:end_period]) / sum(loads)
def SolvePartition(inputs, scenario, start_period, end_period,
inv_mult=0.0, upper_bound = False, mipgap=0.05,
reslim=3600, test=False, design_mults = [0,0],
IFS = None, batPartsMinus = [0.0,0.25,0.5,0.75,1.0],
batPartsPlus = [0.0,0.25,0.5,0.75,1.0], boundary_soc = 0.5,
output=False, amortize_on_demand = True, min_PV=0, procs=1, mincap=0):
"""creates a full partition of the model.
start_period -- starting period for the model
end_period -- ending period for the model
inv_mult -- price of SOC constraint violation (start = end = reset point)
upper_bound -- indicator of whether the upper bound or lower
bound is to be solved
rhsmin -- input from the scenario - this is not yet in
InputReader
batParts -- fraction of max current over which the McCormick underestimators
for current operate. Default values are evenly spaced on the [0,1]
interval but our input comes from the linear model solution and is the
25th,50th, and 75th percentiles of current (as well as the min and max
allowable).
retval -- cplex solution and objective value
"""
numBatParts = len(batPartsPlus)-1
technologies = inputs["technologies"]
generators = [tech for tech in technologies if tech.GetType() == "DieselGenerator"]
batteries = [tech for tech in technologies if tech.GetType() == "Battery"]
pv_arrays = [tech for tech in technologies if tech.GetType() == "PVArray"]
tech_maxes = inputs["tech_maxes"][scenario]
scalars = inputs["scalars"]
loads = scipy.array(inputs["loads"][scenario][
start_period-1:end_period])
pvs = inputs["pv_avail"][scenario]
fuel_costs = scipy.array(inputs["fuel_costs"][scenario])
tech_maxes = inputs["tech_maxes"][scenario]
mingens = inputs["cuts"][scenario]['rhsmin']
num_periods = end_period+1-start_period
prob = 1.0*num_periods/8760
for tech in technologies:
if tech.GetType() != "PVArray":
tech.SetTechMax(tech_maxes[tech.GetName()])
else:
tech.SetPVAvailability(pvs[tech.GetName()])
tech.ConvertPVAvailability(len(inputs["loads"][scenario]))
W_init = inputs["W_init"]
X_init = inputs["X_init"]
#print technologies[0].GetType()
#print tech_maxes
#initialize problem and suppress console output
p = cplex.Cplex()
p.set_error_stream(None)
p.set_warning_stream(None)
if not output:
p.set_log_stream(None)
p.set_results_stream(None)
else:
p.set_log_stream(scenario+"-"+str(start_period)+"_log.txt")
if upper_bound:
resfilename = scenario+"-"+str(start_period)+"_UB.txt"
else:
resfilename = scenario+"-"+str(start_period)+"_LB.txt"
p.set_results_stream(resfilename)
p.parameters.timelimit.set(reslim)
p.parameters.workmem.set(50)
p.parameters.mip.tolerances.mipgap.set(mipgap)
p.parameters.threads.set(procs)
p.parameters.lpmethod.set(4)
p.parameters.mip.strategy.rinsheur.set(10)
p.parameters.mip.strategy.heuristicfreq.set(100)
p.parameters.mip.strategy.file.set(2)
#p.parameters.simplex.tolerances.feasibility.set(0.0001)
p.parameters.emphasis.mip.set(2)
p.parameters.mip.strategy.branch.set(1)
def flatten(l):
out = []
for item in l:
if isinstance(item, (list, tuple)):
out.extend(flatten(item))
else:
out.append(item)
return out
def getName(name, *args):
return '%s_%s'%(name, args)
#define decision variable names
def W_var(tech,k): return "W_"+tech.GetName()+".K"+str(k)
def X_var(pv): return "X_"+pv.GetName()
def P_minus_var(tech,k,t): return "P_minus_" + tech.GetName()+".K" + str(k) + ".TT" + str(t)
def P_plus_var(tech,k,t): return "P_plus_" + tech.GetName()+".K" + str(k) + ".TT" + str(t)
def P_PV_var(pv,t): return "P_PV_"+pv.GetName()+".TT"+str(t)
def F_tilde_var(t): return "F_tilde_TT"+str(t)
def soc_start_var(bat,k): return "soc_start_"+bat.GetName() + ".K" + str(k)
def B_soc_var(bat,k,t):
if t == start_period-1:
return soc_start_var(bat,k)
return "B_soc_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def soc_end_var(bat,k): return B_soc_var(bat,k,end_period)
def I_minus_var(bat,k,t): return "I_minus_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def I_plus_var(bat,k,t): return "I_plus_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def V_soc_var(bat,k,t): return "V_soc_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def Z_minus_var(bat,k,t): return "Z_minus_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def Z_plus_var(bat,k,t): return "Z_plus_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def B_minus_var(bat,k,t): return "B_minus_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def B_plus_var(bat,k,t): return "B_plus_" + bat.GetName() + ".K" + str(k) + ".TT" + str(t)
def G_var(gen,k,t): return "G_" + gen.GetName()+".K" + str(k) + ".TT" + str(t)
def lambda_minus_var(bat,k,n,t): return "lambda_minus_"+bat.GetName() + ".K" + str(k) + ".N"+ str(n) + ".TT" + str(t)
def lambda_plus_var(bat,k,n,t): return "lambda_plus_"+bat.GetName() + ".K" + str(k) + ".N"+ str(n) + ".TT" + str(t)
W_names = flatten([["W_" + tech.GetName() + ".K" + str(i+1)
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() != "PVArray"])
X_names = ["X_" + tech.GetName() for tech in technologies
if tech.GetType() == "PVArray"]
P_minus_names = [[["P_minus_" + tech.GetName()+".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() != "PVArray"]
for t in range(start_period, end_period+1)]
P_minus_names_gen = [[["P_minus_" + tech.GetName()+".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "DieselGenerator"]
for t in range(start_period, end_period+1)]
P_plus_names = [[["P_plus_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
P_PV_names = [["P_PV_"+tech.GetName()+".TT"+str(t)
for tech in technologies
if tech.GetType() == "PVArray"]
for t in range(start_period, end_period+1)]
F_tilde_names = ["F_tilde_TT"+str(t) for t in range(
start_period, end_period+1)]
B_soc_names = [[["B_soc_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
I_minus_names = [[["I_minus_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
I_plus_names = [[["I_plus_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
Z_minus_names = [[["Z_minus_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
Z_plus_names = [[["Z_plus_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
B_minus_names = [[["B_minus_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
B_plus_names = [[["B_plus_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
G_names = [[["G_" + tech.GetName() + ".K" + str(i+1)
+ ".TT" + str(t) for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "DieselGenerator"]
for t in range(start_period, end_period+1)]
lambda_plus_names = [[[["lambda_plus_" + tech.GetName() + ".K" + str(i+1)
+ ".N" + str(n+1) + ".TT" + str(t)
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies if tech.GetType() == "Battery"]
for n in range(numBatParts)]
for t in range(start_period, end_period+1)]
lambda_minus_names = [[[["lambda_minus_" + tech.GetName() + ".K" + str(i+1)
+ ".N" + str(n+1) + ".TT" + str(t)
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies if tech.GetType() == "Battery"]
for n in range(numBatParts)]
for t in range(start_period, end_period+1)]
soc_start_names = [[soc_start_var(tech,(i+1))
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
soc_end_names = [[soc_end_var(tech,(i+1))
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
Jhat_flat = flatten(P_minus_names)
Bhat_flat = flatten(P_plus_names) #batteries
S_flat = flatten(P_PV_names)
Ghat_flat = flatten(G_names)
lamb_flat = flatten(lambda_plus_names)
soc_start_flat = flatten(soc_start_names)
num_Jhat = len(Jhat_flat)
num_Bhat = len(Bhat_flat)
num_S = len(S_flat)
num_Ghat = len(Ghat_flat)
num_lamb = len(lamb_flat)
num_soc = len(soc_start_flat)
#define parameters that will be used in calculating cost
if amortize_on_demand:
purchase_costs = ( FractionOfDemand(inputs["loads"][scenario],
start_period,end_period) *
scipy.array( flatten( [[tech.GetPurchaseCost()
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() != "PVArray"]) ) ) + design_mults[0]
solar_costs = ( scipy.array([
FractionOfSolar(tech,start_period,end_period) *
tech.GetPurchaseCost()
for tech in technologies
if tech.GetType() == "PVArray"]) ) + design_mults[1]
else:
purchase_costs = prob*scipy.array(flatten([[tech.GetPurchaseCost()
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() != "PVArray"])) + design_mults[0]
solar_costs = prob*scipy.array([tech.GetPurchaseCost()
for tech in technologies
if tech.GetType() == "PVArray"]) + design_mults[1]
lambda_multipliers = scipy.array(flatten([[tech.GetMaxPower()
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]))
max_lambda_mult = lambda_multipliers.max()
lambda_multipliers /= max_lambda_mult
#lifecycle costs for I, Z variables (identical for charge and discharge)
I_costs = [[[float(scalars["tau"])*tech.GetLifeCycleCost()*tech.GetASOC()/(2.*tech.GetReferenceCapacity())
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
Z_costs = [[[float(scalars["tau"])*tech.GetLifeCycleCost()*tech.GetDSOC()/(-2.*tech.GetReferenceCapacity())
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]
for t in range(start_period, end_period+1)]
G_costs = [[[tech.GetLifeCycleCost() for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "DieselGenerator"]
for t in range(start_period, end_period+1)]
#creation of variables
#W_bk -- purchase variables
p.variables.add(obj=purchase_costs,
lb=scipy.zeros_like(purchase_costs),
ub=scipy.ones_like(purchase_costs),
types=[p.variables.type.binary]*len(purchase_costs),
names= flatten(W_names) )
#X_s -- Solar Purchase Costs
p.variables.add(obj=solar_costs,
lb=scipy.zeros_like(solar_costs,dtype=float),
ub=[cplex.infinity]*len(solar_costs),
types=[p.variables.type.continuous]*len(solar_costs),
names= X_names )
#P_minus_jkt -- Power out by variable by time period
p.variables.add(obj=scipy.zeros(num_Jhat,dtype=float),
lb=scipy.zeros(num_Jhat,dtype=float),
ub=[cplex.infinity]*num_Jhat,
types=[p.variables.type.continuous]*num_Jhat,
names=flatten(P_minus_names) )
#P_plus_jkt -- Power out by technology (no solar) by time period
p.variables.add(obj=scipy.zeros(num_Bhat,dtype=float),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=[cplex.infinity]*num_Bhat,
types=[p.variables.type.continuous]*num_Bhat,
names=flatten(P_plus_names) )
#P_PV_st -- Power out by variable by time period
p.variables.add(obj=scipy.zeros_like(S_flat,dtype=float),
lb=scipy.zeros(num_S,dtype=float),
ub=[cplex.infinity]*len(S_flat),
types=[p.variables.type.continuous]*num_S,
names=flatten(P_PV_names) )
#F_tilde_t -- Fuel consumed (gal) by time period
p.variables.add(obj=scipy.array(fuel_costs[start_period-1:end_period]),
lb=scipy.zeros_like(F_tilde_names,dtype=float),
ub=[cplex.infinity]*len(F_tilde_names),
types=[p.variables.type.continuous]*len(F_tilde_names),
names=F_tilde_names )
#B_soc_bkt -- State of charge by battery by time period
p.variables.add(obj=scipy.zeros_like(Bhat_flat,dtype=float),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=scipy.ones(num_Bhat,dtype=float),
types=[p.variables.type.continuous]*num_Bhat,
names=flatten(B_soc_names) )
#I_minus_bkt -- Current out by battery by time period
p.variables.add(obj=scipy.array(flatten(I_costs)),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=[cplex.infinity]*num_Bhat,
types=[p.variables.type.continuous]*num_Bhat,
names=flatten(I_minus_names) )
#I_plus_bkt -- Current in by battery by time period
p.variables.add(obj=scipy.array(flatten(I_costs)),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=[cplex.infinity]*num_Bhat,
types=[p.variables.type.continuous]*num_Bhat,
names=flatten(I_plus_names) )
#Z_minus_bkt -- Current out*State of charge by battery by time period
p.variables.add(obj=scipy.array(flatten(Z_costs)),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=[cplex.infinity]*num_Bhat,
types=[p.variables.type.continuous]*num_Bhat,
names=flatten(Z_minus_names) )
#Z_plus_bkt -- Current in*State of charge by battery by time period
p.variables.add(obj=scipy.array(flatten(Z_costs)),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=[cplex.infinity]*num_Bhat,
types=[p.variables.type.continuous]*num_Bhat,
names=flatten(Z_plus_names) )
#B_minus_bkt -- 1 if battery discharges, 0 o.w. by time period
p.variables.add(obj=scipy.zeros_like(Bhat_flat,dtype=float),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=scipy.ones(num_Bhat,dtype=float),
types=[p.variables.type.binary]*num_Bhat,
names=flatten(B_minus_names) )
#B_plus_bkt -- 1 if battery charges, 0 o.w. by time period
p.variables.add(obj=scipy.zeros_like(Bhat_flat,dtype=float),
lb=scipy.zeros(num_Bhat,dtype=float),
ub=scipy.ones(num_Bhat,dtype=float),
types=[p.variables.type.binary]*num_Bhat,
names=flatten(B_plus_names) )
#G_gkt -- 1 if generator on, 0 o.w. by time period
p.variables.add(obj=scipy.array(flatten(G_costs)),
lb=scipy.zeros(num_Ghat,dtype=float),
ub=scipy.ones(num_Ghat,dtype=float),
types=[p.variables.type.binary]*num_Ghat,
names=flatten(G_names) )
#lambda_plus - 1 if SOC is in given in range and battery is charging, 0 o.w.
p.variables.add(obj=scipy.zeros_like(lamb_flat,dtype=float),
lb=scipy.zeros(num_lamb,dtype=float),
ub=scipy.ones(num_lamb,dtype=float),
types=[p.variables.type.binary]*num_lamb,
names=flatten(lambda_plus_names) )
#lambda_minus - 1 if SOC is in given in range and battery is charging, 0 o.w.
p.variables.add(obj=scipy.zeros_like(lamb_flat,dtype=float),
lb=scipy.zeros(num_lamb,dtype=float),
ub=scipy.ones(num_lamb,dtype=float),
types=[p.variables.type.binary]*num_lamb,
names=flatten(lambda_minus_names) )
#soc_start by scenario
p.variables.add(obj=scipy.zeros(num_soc),
lb=[0.0]*num_soc,
ub=[1.0]*num_soc,
types=[p.variables.type.continuous]*num_soc,
names=flatten(soc_start_names) )
#inventory
p.variables.add(obj=[inv_mult],
lb=[0.0],
ub=[cplex.infinity],
types=[p.variables.type.continuous],
names=['battery_inv'] )
#prioritize branching
orders = []
for gen in generators:
for k in range(tech_maxes[gen.GetName()]):
orders.append((W_var(gen,k+1),1+int(gen.GetName()[1:]),p.order.branch_direction.up))
for bat in batteries:
for k in range(tech_maxes[bat.GetName()]):
orders.append((W_var(bat,k+1),1,p.order.branch_direction.up))
p.order.set(orders)
#minimize cost
p.objective.set_sense( p.objective.sense.minimize )
#constraint 15a - power flow
val = flatten([[tech.GetEfficiencyOut()
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() != "PVArray"])
val.extend( [1.0
for tech in technologies
if tech.GetType() == "PVArray"] )
val.extend(flatten([[ -1.0
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"]))
p.linear_constraints.add(lin_expr=[
cplex.SparsePair(flatten(P_minus_names[t]+
P_PV_names[t]+P_plus_names[t]), val)
for t in range(num_periods)],
senses=['G' for t in range(num_periods)],
rhs=loads,
names=['Sys_Op_15a_'+str(t+start_period)
for t in range(num_periods)])
#constraint 15b - spinning reserve
#eta_out*p_max*Bsoc for all batteries in time t
val = flatten([[ tech.GetEfficiencyOut()*tech.GetMaxPower()*
tech.GetSOC()
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "Battery"])
#p_max*G for all generators in time t
val.extend(flatten([[ tech.GetMaxPower()
for i in range(tech_maxes[tech.GetName()])]
for tech in technologies
if tech.GetType() == "DieselGenerator"]))
#-P_minus for all generators in time t
val.extend(scipy.ones(int(num_Ghat/num_periods)))
#-k_sol*P_solar
val.extend(-1.0*float(scalars["k_sol"])*scipy.ones(int(num_S/num_periods),dtype=float))
p.linear_constraints.add(lin_expr=[
cplex.SparsePair(flatten(B_soc_names[t]+
G_names[t]+P_minus_names_gen[t]+
P_PV_names[t]), val)
for t in range(num_periods)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Sys_Op_15b_'+str(t+start_period)
for t in range(num_periods)])
#constraint 15c -- break purchasing symmetry
for tech in technologies:
if tech.GetType() != "PVArray":
for i in range(tech_maxes[tech.GetName()]-1):
ind = ["W_" + tech.GetName() + ".K" + str(i+1),
"W_" + tech.GetName() + ".K" + str(i+2)]
val = [1,-1]
p.linear_constraints.add(lin_expr=[
cplex.SparsePair( ind,val )],
senses = ['G'],
rhs = [0],
names = ['Sys_Op_15c_'+tech.GetName()+
".K"+str(i)])
### Generator Operations
#constraint 16a -- Generator Max Power
for gen in generators:
for k in range(tech_maxes[gen.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([G_var(gen,k+1,t+start_period),
P_minus_var(gen,k+1,(t+start_period))],
[-1*gen.GetMaxPower(),1])
for t in range(num_periods)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods,dtype=float),
names=['Gen_Op_16a1_'+gen.GetName()+".K"
+str(k+1)+".TT"+str(t+start_period)
for t in range(num_periods)])
#constraint 16a2 -- Generator Min Power
for gen in generators:
for k in range(tech_maxes[gen.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([G_var(gen,k+1,t+start_period),
P_minus_var(gen,k+1,(t+start_period))],
[-1*gen.GetMinPower(),1])
for t in range(num_periods)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods,dtype=float),
names=['Gen_Op_16a2_'+gen.GetName()+".K"
+str(k+1)+".TT"+str(t+start_period)
for t in range(num_periods)])
#constraint 16b -- Fuel Usage
val = [1]
val.extend(flatten([[gen.GetFuelUseB()/-1000.0 for i in range(tech_maxes[gen.GetName()])]
for gen in generators] ) )
val.extend(flatten([[-1.0*gen.GetFuelUseC() for i in range(tech_maxes[gen.GetName()])]
for gen in generators] ))
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([F_tilde_names[t]]+
flatten(P_minus_names_gen[t]
+ G_names[t] ), val)
for t in range(num_periods)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods,dtype=float),
names=['Gen_Op_16b_'+str(t+start_period)
for t in range(num_periods)])
#constraint 16c -- Use only generators that are purchased
for gen in generators:
for k in range(tech_maxes[gen.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([
"G_" + gen.GetName()
+ ".K" + str(k+1)
+ ".TT" + str(t+start_period), "W_" +
gen.GetName() + ".K" + str(k+1)],[1,-1])
for t in range(num_periods)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods,dtype=float),
names=['Gen_Op_16c_'+gen.GetName()+".K"
+str(k+1)+".TT"+str(t+start_period)
for t in range(num_periods)])
#constraint 16d -- Break generator power out symmetry
for gen in generators:
for k in range(tech_maxes[gen.GetName()]-1):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([
"P_minus_" + gen.GetName() + ".K" + str(k+1)
+ ".TT" + str(t+start_period),
"P_minus_" + gen.GetName()
+ ".K" + str(k+2)
+ ".TT" + str(t+start_period)],[1,-1])
for t in range(num_periods)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods,dtype=float),
names=['Gen_Op_16d_'+gen.GetName()+".K"
+str(k+2)+".TT"+str(t+start_period)
for t in range(num_periods)])
#constraint 16e -- Break generator use symmetry
for gen in generators:
for k in range(tech_maxes[gen.GetName()]-1):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([
"G_" + gen.GetName() + ".K" + str(k+1)
+ ".TT" + str(t+start_period),
"G_" + gen.GetName()
+ ".K" + str(k+2)
+ ".TT" + str(t+start_period)],[1,-1])
for t in range(num_periods)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods,dtype=float),
names=['Gen_Op_16d_'+gen.GetName()+".K"
+str(k+2)+".TT"+str(t+start_period)
for t in range(num_periods)])
#constraint 17a -- PV out limited by solar power and # purchased
for pv in pv_arrays:
p.linear_constraints.add(lin_expr=[
cplex.SparsePair(["P_PV_"+pv.GetName()
+ ".TT"+str(t+start_period),"X_"+pv.GetName()],
[1.0,
-1.0*pv.CalculatePowerAvailable(t+start_period-1)])
for t in range(num_periods)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods,dtype=float),
names=['PV_Op_17a_'+pv.GetName()
+ ".TT"+str(t+start_period)
for t in range(num_periods)]
)
#constraint 17b -- upper bound on purchases
for pv in pv_arrays:
p.linear_constraints.add(lin_expr=[
cplex.SparsePair(["X_"+pv.GetName()],
[1.0])],
senses=['L'],
rhs=[75],#[float(scalars["solar_max"])],
names=['PV_Op_17b_'+pv.GetName()]
)
#constraints 18a, 18b use Z in the place of B_soc*I_plus, substituted via
#constraints 23-24, which are not implemented here for efficiency.
#constraint Linear_18a: Linearization of P_plus (Z replaces B_soc*I_plus)
for bat in batteries:
val = [1,
-1.0*bat.GetVoltageA(),
-1.0*bat.GetVoltageB()-(bat.GetAvgCurrent()*
bat.GetResistance())]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(
lin_expr=[cplex.SparsePair([
P_plus_var(bat,k+1,t),
Z_plus_var(bat,k+1,t),
I_plus_var(bat,k+1,t)]
,val) for t in range(start_period,
end_period+1)],
senses=['E' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Linear_18a_'+bat.GetName()+".K"+str(k+1)
+".TT"+str(t) for t in range(start_period,
end_period+1)])
#constraint Linear_18b: Linearization of P_minus (Z replaces B_soc*I_minus)
for bat in batteries:
val = [1,
-1.0*bat.GetVoltageA(),
-1.0*bat.GetVoltageB()+(bat.GetAvgCurrent()*
bat.GetResistance())]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(
lin_expr=[cplex.SparsePair([
P_minus_var(bat,k+1,t),
Z_minus_var(bat,k+1,t),
I_minus_var(bat,k+1,t)]
,val) for t in range(start_period,
end_period+1)],
senses=['E' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Linear_18b_'+bat.GetName()+".K"+str(k+1)
+".TT"+str(t) for t in range(start_period,
end_period+1)])
#constraint 18c -- State of charge tracking
for bat in batteries:
val = [1.0,-1.0,-1.0*(
float(scalars["tau"])*bat.GetEfficiencyIn()
/ bat.GetReferenceCapacity()),
1.0*(float(scalars["tau"]) / bat.GetReferenceCapacity())]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([B_soc_var(bat,k+1,t),
B_soc_var(bat,k+1,t-1),
I_plus_var(bat,k+1,t),
I_minus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['E' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18c_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18d1 -- SOC maximum (note: includes soc_start)
val = [1,-1.0*float(scalars["soc_max"])]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([B_soc_var(bat,k+1,t),
W_var(bat,k+1)]
,val) for t in range(start_period-1,end_period+1)],
senses=['L' for t in range(num_periods+1)],
rhs=scipy.zeros(num_periods+1),
names=['Bat_Op_18d1_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period-1,end_period+1)])
for bat in batteries:
#constraint 18d2 -- SOC minimum (note: includes soc_start)
val = [1,-1.0*float(scalars["soc_min"])]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([B_soc_var(bat,k+1,t),
W_var(bat,k+1)]
,val) for t in range(start_period-1,end_period+1)],
senses=['G' for t in range(num_periods+1)],
rhs=scipy.zeros(num_periods+1),
names=['Bat_Op_18d2_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period-1,end_period+1)])
for bat in batteries:
#constraint 18e -- SOC equal for all batteries of type b
val = [1.0,-1.0,1.0]
for k in range(tech_maxes[bat.GetName()]-1):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([B_soc_var(bat,k+1,t),
B_soc_var(bat,k+2,t),
W_var(bat,k+1)]
,val) for t in range(start_period,end_period+1)],
senses=['L' for t in range(num_periods+1)],
rhs=1.0*scipy.ones(num_periods),
names=['Bat_Op_18e_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18f -- SOC equal for all batteries of type b
val = [1.0,1.0,-1.0]
for k in range(tech_maxes[bat.GetName()]-1):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([B_soc_var(bat,k+1,t),
B_soc_var(bat,k+2,t),
W_var(bat,k+1)]
,val) for t in range(start_period,end_period+1)],
senses=['G' for t in range(num_periods)],
rhs=-1.0*scipy.ones(num_periods),
names=['Bat_Op_18f_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
#constraint 18g -- tracks starting storage inventory
ind = ['battery_inv'] #R^ell
val = [-1.0]
for bat in batteries:
for k in range(1,tech_maxes[bat.GetName()]+1):
ind.append(soc_start_var(bat,k))
val.append(bat.GetReferenceCapacity())
p.linear_constraints.add(
lin_expr=[cplex.SparsePair(ind,val)],
senses=['E'],
rhs=[0],
names=['INVENTORY_18g'])
#constraint 18h -- tracks ending storage inventory
ind = ['battery_inv']
val = [-1.0]
for bat in batteries:
for k in range(1,tech_maxes[bat.GetName()]+1):
ind.append(soc_end_var(bat,k))
val.append(bat.GetReferenceCapacity())
p.linear_constraints.add(
lin_expr=[cplex.SparsePair(ind,val)],
senses=['E'],
rhs=[0],
names=['INVENTORY_18h'])
for bat in batteries:
#constraint 18i1 -- power out upper limits of battery type b
val = [1.0,-1.0*bat.GetMaxPower()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([P_plus_var(bat,k+1,t),
B_plus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18i1_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18i2 -- power in lower limits of battery type b
val = [1.0,-1.0*bat.GetMinPower()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([P_plus_var(bat,k+1,t),
B_plus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18i2_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18j1 -- power in upper limits of battery type b
val = [1.0,-1.0*bat.GetMaxPower()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([P_minus_var(bat,k+1,t),
B_minus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18j1_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18j2 -- power out lower limits of battery type b
val = [1.0,-1.0*bat.GetMinPower()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([P_minus_var(bat,k+1,t),
B_minus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18j2_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18k1 -- current in upper limits (semicontinuous)
val = [1.0,-1.0*bat.GetIUPlus()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([I_plus_var(bat,k+1,t),
B_plus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18k1_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18k2 -- current in lower limits (semicontinuous)
val = [1.0,-1.0*bat.GetMinCurrent()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([I_plus_var(bat,k+1,t),
B_plus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18k2_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18l1 -- current out upper limits (semicontinuous)
val = [1.0,-1.0*bat.GetIUMinus()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([I_minus_var(bat,k+1,t),
B_minus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18l1_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18l2 -- current out upper limits (semicontinuous)
val = [1.0,-1.0*bat.GetMinCurrent()]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([I_minus_var(bat,k+1,t),
B_minus_var(bat,k+1,t)]
,val) for t in range(start_period,end_period+1)],
senses=['G' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18l2_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18m -- current out upper limits (bound by SOC)
val = [1.0,-1.0*(bat.GetIUMinus())]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([I_minus_var(bat,k+1,t),
B_soc_var(bat,k+1,t-1)]
,val) for t in range(start_period,end_period+1)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18m_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18n -- Only use batteries that you buy
val = [1,1,-1]
for k in range(tech_maxes[bat.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([B_minus_var(bat,k+1,t),
B_plus_var(bat,k+1,t),
W_var(bat,k+1)],val)
for t in range(start_period,end_period+1)],
senses=['L' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Bat_Op_18n_'+bat.GetName()+".K"+str(k+1) +
".TT"+str(t) for t in range(start_period,end_period+1)])
for bat in batteries:
#constraint 18o -- Can't simultaneously charge and discharge batteries
val=[1,1]
for batp in batteries:
if batp != bat:
for k in range(tech_maxes[bat.GetName()]):
for kp in range(tech_maxes[batp.GetName()]):
p.linear_constraints.add(lin_expr=[
cplex.SparsePair([B_plus_var(bat,k+1,t),
B_minus_var(batp,kp+1,t)],val)
for t in range(
start_period,end_period+1)],
senses=['L' for t in range(num_periods)],
rhs=scipy.ones(num_periods,dtype=float),
names=['Bat_Op_18o_'+bat.GetName()+".K"+str(k+1)
+".BP"+batp.GetName()[-1]+
".KP"+str(kp+1)+".TT"+str(t)
for t in range(start_period,end_period+1)])
#Constraint 19a: Nonanticipativity of W
#Fix purchase decision if running the upper bound model
if upper_bound:
inds = []
vals = []
for tech in technologies:
if tech.GetType() != "PVArray":
for k in range(1,tech_maxes[tech.GetName()]+1):
inds.append(W_var(tech,k))
if tech.GetName() in W_init[scenario].keys():
if "K"+str(k) in W_init[scenario][tech.GetName()].keys():
vals.append(W_init[scenario][tech.GetName()]["K"+str(k)])
else: vals.append(0)
else: vals.append(0)
#print inds, vals
p.variables.set_upper_bounds(zip(inds,vals))
p.variables.set_lower_bounds(zip(inds,vals))
#Constraint 19b: Nonanticipativity of X
#Fix purchase decision if running the upper bound model
if upper_bound:
inds = []
vals = []
for tech in technologies:
if tech.GetType() == "PVArray":
inds.append(X_var(tech))
if tech.GetName() in X_init[scenario].keys():
vals.append(X_init[scenario][tech.GetName()])
else: vals.append(0)
#print inds, vals
p.variables.set_upper_bounds(zip(inds,vals))
p.variables.set_lower_bounds(zip(inds,vals))
#Constraint 19c: Nonanticipativity of R^\ell. This is enforced by
#fixing the starting state of charge for all batteriesin the upper bound.
#model, and is relaxed in the lower bound model.
if upper_bound and start_period != 1:
val = [1.0,-1.0*boundary_soc]
sense = ['E']
for bat in batteries:
for k in range(1,tech_maxes[bat.GetName()]+1):
p.linear_constraints.add(
lin_expr=[cplex.SparsePair([soc_start_var(bat,k),W_var(bat,k)],
val)],
senses=sense,
rhs=[0],
names=['Storage_inv_start_UB_19c1'+bat.GetName()+".K"+str(k)])
if upper_bound and start_period != 1:
val = [1.0,-1.0*boundary_soc]
sense = ['E']
ending = 'UB_'
for bat in batteries:
for k in range(1,tech_maxes[bat.GetName()]+1):
p.linear_constraints.add(
lin_expr=[cplex.SparsePair([soc_end_var(bat,k),W_var(bat,k)],
val)],
senses=sense,
rhs=[0],
names=['Storage_inv_end_UB_19c2'+bat.GetName()+".K"+str(k)])
#Constraint 20: boundary condition for battery state-of-charge
if start_period == 1:
val = [1.0,-1.0*scalars["b_init"]]
sense = ['E']
for bat in batteries:
for k in range(1,tech_maxes[bat.GetName()]+1):
p.linear_constraints.add(
lin_expr=[cplex.SparsePair([soc_start_var(bat,k),W_var(bat,k)],
val)],
senses=sense,
rhs=[0],
names=['Storage_inv_boundary_'+bat.GetName()+".K"+str(k)])
#constraints (21) denote variable bounds
#constraints (22)-(24) not directly implemented
def i_u_part_minus(bat,n):
"""
This defines:
i^{L-}_{bn} = i_u_part_minus(bat,n-1), and
i^{U-}_{bn} = i_u_part_minus(n)
"""
return bat.GetMinCurrent() + batPartsMinus[n]*(bat.GetIUMinus()-bat.GetMinCurrent())
def i_u_part_plus(bat,n):
"""
This defines:
i^{L+}_{bn} = i_u_part_plus(bat,n-1), and
i^{U+}_{bn} = i_u_part_plus(n)
"""
return bat.GetMinCurrent() + batPartsPlus[n]*(bat.GetIUPlus()-bat.GetMinCurrent())
#constraint 25a -- one lambda per BKT - reconcile plus.
val = [1.0 for i in range(1,numBatParts+1)]+[-1.0]
for bat in batteries:
for k in range(1,tech_maxes[bat.GetName()]+1):
p.linear_constraints.add(
lin_expr=[cplex.SparsePair([lambda_plus_var(bat,k,n,t)
for n in range(1,numBatParts+1)]+[B_plus_var(bat,k,t)],
val) for t in range(start_period,
end_period+1)],
senses=['E' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Linear_25a_'+bat.GetName()+".K"+str(k)+
".TT"+str(t) for t in range(start_period,
end_period+1)])
#constraint 25b -- one lambda per BKT - reconcile minus.
for bat in batteries:
for k in range(1,tech_maxes[bat.GetName()]+1):
p.linear_constraints.add(
lin_expr=[cplex.SparsePair([lambda_minus_var(bat,k,n,t)
for n in range(1,numBatParts+1)]+[B_minus_var(bat,k,t)],
val) for t in range(start_period,
end_period+1)],
senses=['E' for t in range(num_periods)],
rhs=scipy.zeros(num_periods),
names=['Linear_25b_'+bat.GetName()+".K"+str(k)+
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