def createVar(mod, PdDict, QdDict, PpvDict, QpvDict, PwtDict, QwtDict, PG2Dict,
QG2Dict, PC1Dict, QC1Dict):
# Import parameters and configuration
Time = cf.Time()
ElecSys = cf.ElecSys()
Gen = cf.Gen()
CoGen = cf.CoGen()
PhoArr = cf.PhoArr()
WindTur = cf.WindTur()
WatPump = cf.WatPump()
HeatPump = cf.HeatPump()
# Decision variables for electric power system
Pflow = mod.addVars(Time.serie,
ElecSys.branch,
lb=0.0,
ub=GRB.INFINITY,
name='Pflow')
Qflow = mod.addVars(Time.serie,
ElecSys.branch,
lb=0.0,
ub=GRB.INFINITY,
name='Qflow')
BranCur = mod.addVars(Time.serie,
ElecSys.branch,
lb=0.0,
ub=appendTime(ElecSys.Imax),
name='BranCur')
Pinje = mod.addVars(Time.serie,
ElecSys.bus,
lb=-GRB.INFINITY,
ub=GRB.INFINITY,
name='Pinje')
Qinje = mod.addVars(Time.serie,
ElecSys.bus,
lb=-GRB.INFINITY,
ub=GRB.INFINITY,
name='Qinje')
Vol = mod.addVars(Time.serie,
ElecSys.bus,
lb=appendTime(ElecSys.Vmin),
ub=appendTime(ElecSys.Vmax),
name='Vol')
PGen = mod.addVars(Time.serie,
Gen.name,
lb=appendTime(Gen.Pmin),
ub=appendTime(Gen.Pmax),
name='PGen')
QGen = mod.addVars(Time.serie,
Gen.name,
lb=appendTime(Gen.Qmin),
ub=appendTime(Gen.Qmax),
name='QGen')
PCoGen = mod.addVars(Time.serie,
CoGen.name,
lb=appendTime(CoGen.Pmin),
ub=appendTime(CoGen.Pmax),
name='PCoGen')
QCoGen = mod.addVars(Time.serie,
CoGen.name,
lb=appendTime(CoGen.Qmin),
ub=appendTime(CoGen.Qmax),
name='QCoGen')
PPhoArr = mod.addVars(Time.serie,
PhoArr.name,
lb=appendTime(PhoArr.Pmin),
ub=appendTime(PhoArr.Pmax),
name='PPhoArr')
QPhoArr = mod.addVars(Time.serie,
PhoArr.name,
lb=appendTime(PhoArr.Qmin),
ub=appendTime(PhoArr.Qmax),
name='QPhoArr')
PWindTur = mod.addVars(Time.serie,
WindTur.name,
lb=appendTime(WindTur.Pmin),
ub=appendTime(WindTur.Pmax),
name='PWindTur')
QWindTur = mod.addVars(Time.serie,
WindTur.name,
lb=appendTime(WindTur.Qmin),
ub=appendTime(WindTur.Qmax),
name='QWindTur')
PWatPump = mod.addVars(Time.serie,
WatPump.name,
lb=appendTime(WatPump.Pmin),
ub=appendTime(WatPump.Pmax),
name='PWatPump')
PHeatPump = mod.addVars(Time.serie,
HeatPump.name,
lb=appendTime(HeatPump.Pmin),
ub=appendTime(HeatPump.Pmax),
name='PHeatPump')
return Pflow, Qflow, BranCur, Pinje, Qinje, Vol, PGen, QGen, PCoGen, QCoGen, PPhoArr, QPhoArr, PWindTur, QWindTur, \
PWatPump, PHeatPump
def opf(PdDict, QdDict, PpvDict, QpvDict, PwtDict, QwtDict, PG2Dict, QG2Dict, PC1Dict, QC1Dict, VolDict, ThetaDict):
# Import parameters and configuration
Time = cf.Time()
ElecSys = cf.ElecSys()
Gen = cf.Gen()
CoGen = cf.CoGen()
# Create optimization model
mod = Model('OPF')
# Create model variables
Pflow, Qflow, BranCur, Pinje, Qinje, Vol, PGen, QGen, PCoGen, QCoGen, PPhoArr, QPhoArr, PWindTur, QWindTur, \
PWatPump, PHeatPump = md.createVar(mod, PdDict, QdDict, PpvDict, QpvDict, PwtDict, QwtDict, PG2Dict, QG2Dict, PC1Dict, QC1Dict, VolDict, ThetaDict)
# Create model constraints
md.CreateConstr(mod, PdDict, QdDict, PpvDict, QpvDict, PwtDict, QwtDict, PG2Dict, QG2Dict, PC1Dict, QC1Dict, VolDict, ThetaDict, \
Pflow, Qflow, BranCur, Pinje, Qinje, Vol, PGen, QGen, PCoGen, QCoGen, PPhoArr, QPhoArr, PWindTur, QWindTur, \
PWatPump, PHeatPump )
# Set objective
obj = LinExpr()
for t in Time.serie:
for i in Gen.name:
obj = obj + PGen[t,i]*Gen.cost[i]
for i in CoGen.name:
obj = obj + PCoGen[t,i]*CoGen.cost[i]
mod.setObjective(obj, GRB.MINIMIZE)
# Output model
mod.update()
# Compute optimal solution
mod.optimize()
# Get optimized solutions
Sol_PGen = mod.getAttr('X', PGen)
Sol_PCoGen = mod.getAttr('X', PCoGen)
Sol_PPhoArr = mod.getAttr('X', PPhoArr)
Sol_PWindTur = mod.getAttr('X', PWindTur)
Sol_PWatPump = mod.getAttr('X', PWatPump)
Sol_PHeatPump = mod.getAttr('X', PHeatPump)
Sol_Vol = mod.getAttr('X', Vol)
Sol_BranCur = mod.getAttr('X', BranCur)
Sol_Pflow = mod.getAttr('X', Pflow)
Sol_Qflow = mod.getAttr('X', Qflow)
# Display optimal solution
plt.close('all')
font = {'family' : 'sans-serif',
'style' : 'normal',
'weight' : 'bold',
'size' : 22}
text = {'usetex' : True}
matplotlib.rc('font', **font)
matplotlib.rc('text', **text)
# Active power balance of generation in a stacked bar graph
plt.figure()
width = 0.65
plt.title('Active power balance: supply')
#plt.bar(Time.serie, Sol_PGen.select('*','G1'), width, bottom=None, label=r'$P^{\rm{G}}_{1,t}$')
# plt.bar(Time.serie, Sol_PGen.select('*','G2'), width, bottom=Sol_PGen.select('*','G1'), label=r'$P^{\rm{G}}_{2,t}$')
plt.bar(Time.serie, Sol_PGen.select('*','G2'), width, bottom=None, label=r'$P^{\rm{G}}_{2,t}$')
plt.bar(Time.serie, Sol_PCoGen.select('*','C1'), width, \
#bottom=[sum(x) for x in zip(Sol_PGen.select('*','G1'),Sol_PGen.select('*','G2'))], label=r'$P^{\rm{C}}_{1,t}$')
bottom=[sum(x) for x in zip(Sol_PGen.select('*','G2'))], label=r'$P^{\rm{C}}_{1,t}$')
plt.bar(Time.serie, Sol_PPhoArr.select('*','P1'), width, \
# bottom=[sum(x) for x in zip(Sol_PGen.select('*','G1'),Sol_PGen.select('*','G2'), \
# Sol_PCoGen.select('*','C1'))], label=r'$P^{\rm{P}}_{1,t}$')
bottom=[sum(x) for x in zip(Sol_PGen.select('*','G2'), \
Sol_PCoGen.select('*','C1'))], label=r'$P^{\rm{P}}_{1,t}$')
plt.bar(Time.serie, Sol_PWindTur.select('*','W1'), width, \
# bottom=[sum(x) for x in zip(Sol_PGen.select('*','G1'),Sol_PGen.select('*','G2'), \
# Sol_PCoGen.select('*','C1'),Sol_PPhoArr.select('*','P1'))], label=r'$P^{\rm{W}}_{1,t}$')
bottom=[sum(x) for x in zip(Sol_PGen.select('*','G2'), \
Sol_PCoGen.select('*','C1'),Sol_PPhoArr.select('*','P1'))], label=r'$P^{\rm{W}}_{1,t}$')
plt.bar(Time.serie, Sol_PPhoArr.select('*','P2'), width, \
# bottom=[sum(x) for x in zip(Sol_PGen.select('*','G1'),Sol_PGen.select('*','G2'), \
# Sol_PCoGen.select('*','C1'),Sol_PPhoArr.select('*','P1'), \
# Sol_PWindTur.select('*','W1'))], label=r'$P^{\rm{P}}_{2,t}$')
bottom=[sum(x) for x in zip(Sol_PGen.select('*','G2'), \
Sol_PCoGen.select('*','C1'),Sol_PPhoArr.select('*','P1'), \
Sol_PWindTur.select('*','W1'))], label=r'$P^{\rm{P}}_{2,t}$')
#plt.bar(Time.serie, Sol_PWindTur.select('*','W2'), width, \
# bottom=[sum(x) for x in zip(Sol_PGen.select('*','G1'),Sol_PGen.select('*','G2'), \
# Sol_PCoGen.select('*','C1'),Sol_PPhoArr.select('*','P1'), \
# Sol_PWindTur.select('*','W1'),Sol_PPhoArr.select('*','P2'))], label=r'$P^{\rm{W}}_{2,t}$')
plt.legend()
plt.xlabel('time $t$ (60-min step)')
plt.ylabel('Power $P$ (MW)')
plt.grid(linestyle='--')
# Active power balance of loads in a stacked bar graph
plt.figure()
plt.title('Active power balance: demand')
plt.bar(Time.serie, Sol_PWatPump.select('*','WP1'), width, bottom=None, label=r'$P^{\rm{WP}}_{1,t}$')
plt.bar(Time.serie, Sol_PHeatPump.select('*','HP1'), width, bottom=Sol_PWatPump.select('*','WP1'), label=r'$P^{\rm{HP}}_{1,t}$')
plt.bar(Time.serie, [sum([PdDict[t,j] for j in ElecSys.bus]) for t in Time.serie], width, \
bottom=[sum(x) for x in zip(Sol_PWatPump.select('*','WP1'),Sol_PHeatPump.select('*','HP1'))], label=r'$P^{\rm{D}}_{t}$')
Ploss = []
for t in Time.serie:
Ploss.append(-1*ElecSys.baseMVA*sum( [ElecSys.Zr[i,j]*Sol_BranCur[t,i,j] for (i,j) in ElecSys.branch] ))
plt.bar(Time.serie, [-x for x in Ploss], width, \
bottom=[sum(x) for x in zip(Sol_PWatPump.select('*','WP1'),Sol_PHeatPump.select('*','HP1'), \
[sum([PdDict[t,j] for j in ElecSys.bus]) for t in Time.serie])], label=r'$P^{\rm{loss}}_{t}$')
plt.legend()
plt.xlabel('time $t$ (60-min step)')
plt.ylabel('Power $P$ (MW)')
plt.grid(linestyle='--')
# Voltage profile
# plt.figure()
# plt.title('Voltage profile')
# plt.step(Time.serie, Sol_Vol.select('*',1),'r-', where='mid', label='$v_{1}$')
# plt.step(Time.serie, Sol_Vol.select('*',18),'b-', where='mid', label='$v_{18}$')
# plt.step(Time.serie, Sol_Vol.select('*',22),'g-', where='mid', label='$v_{22}$')
# plt.step(Time.serie, Sol_Vol.select('*',25),'k-', where='mid', label='$v_{25}$')
# plt.step(Time.serie, Sol_Vol.select('*',33),'m-', where='mid', label='$v_{33}$')
# plt.legend()
# plt.xlabel('time $t$ (60-min step)')
# plt.ylabel('Voltage $v$ (V)')
# plt.grid(linestyle='--')
plt.show()
def CreateConstr(mod, PdDict, QdDict, PpvDict, QpvDict, PwtDict, QwtDict, PG2Dict, QG2Dict, PC1Dict, QC1Dict, \
Pflow, Qflow, BranCur, Pinje, Qinje, Vol, PGen, QGen, PCoGen, QCoGen, PPhoArr, QPhoArr, PWindTur, QWindTur, \
PWatPump, PHeatPump):
# Import parameters and configuration
Time = cf.Time()
ElecSys = cf.ElecSys()
Gen = cf.Gen()
CoGen = cf.CoGen()
PhoArr = cf.PhoArr()
WindTur = cf.WindTur()
WatPump = cf.WatPump()
HeatPump = cf.HeatPump()
# Nodal power balance
mod.addConstrs(( sum( [ PGen[t,j] for j in Gen.name if Gen.bus[j] == i ] ) + \
sum( [ PCoGen[t,j] for j in CoGen.name if CoGen.bus[j] == i ] ) + \
sum( [ PPhoArr[t,j] for j in PhoArr.name if PhoArr.bus[j] == i ] ) + \
sum( [ PWindTur[t,j] for j in WindTur.name if WindTur.bus[j] == i ] ) == \
sum( [ PWatPump[t,j] for j in WatPump.name if WatPump.bus[j] == i ] ) + \
sum( [ PHeatPump[t,j] for j in HeatPump.name if HeatPump.bus[j] == i ] ) + \
PdDict[t,i] + Pinje[t,i] \
for t in Time.serie for i in ElecSys.bus ), name='PNdBal')
mod.addConstrs(( sum( [ QGen[t,j] for j in Gen.name if Gen.bus[j] == i ] ) + \
sum( [ QCoGen[t,j] for j in CoGen.name if CoGen.bus[j] == i ] ) + \
sum( [ QPhoArr[t,j] for j in PhoArr.name if PhoArr.bus[j] == i ] ) + \
sum( [ QWindTur[t,j] for j in WindTur.name if WindTur.bus[j] == i ] ) == \
QdDict[t,i] + Qinje[t,i] \
for t in Time.serie for i in ElecSys.bus ), name='QNdBal')
# Ramping constraints
# mod.addConstrs(( PGen[t,i]-PGen[t-1,i] <= Gen.DelPmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in Gen.name ), name='GenPRampMax')
# mod.addConstrs(( PGen[t,i]-PGen[t-1,i] >= -Gen.DelPmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in Gen.name ), name='GenPRampMin')
# mod.addConstrs(( QGen[t,i]-QGen[t-1,i] <= Gen.DelQmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in Gen.name ), name='GenQRampMax')
# mod.addConstrs(( QGen[t,i]-QGen[t-1,i] >= -Gen.DelQmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in Gen.name ), name='GenQRampMin')
# mod.addConstrs(( PCoGen[t,i]-PCoGen[t-1,i] <= CoGen.DelPmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in CoGen.name ), name='CoGenPRampMax')
# mod.addConstrs(( PCoGen[t,i]-PCoGen[t-1,i] >= -CoGen.DelPmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in CoGen.name ), name='CoGenPRampMin')
# mod.addConstrs(( QCoGen[t,i]-QCoGen[t-1,i] <= CoGen.DelQmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in CoGen.name ), name='CoGenQRampMax')
# mod.addConstrs(( QCoGen[t,i]-QCoGen[t-1,i] >= -CoGen.DelQmax[i] \
# for t in Time.serie if (t-1) in Time.serie for i in CoGen.name ), name='CoGenQRampMin')
mod.addConstrs(( PHeatPump[t,i]-PHeatPump[t-1,i] <= HeatPump.DelPmax[i] \
for t in Time.serie if (t-1) in Time.serie for i in HeatPump.name ), name='HPPRampMax')
mod.addConstrs(( PHeatPump[t,i]-PHeatPump[t-1,i] >= -HeatPump.DelPmax[i] \
for t in Time.serie if (t-1) in Time.serie for i in HeatPump.name ), name='HPPRampMin')
# Generation constraints of renewable energy
mod.addConstrs((PPhoArr[t, i] <= PpvDict[t, i] for t in Time.serie
for i in PhoArr.name),
name='PpvMax')
mod.addConstrs((PWindTur[t, i] <= PwtDict[t, i] for t in Time.serie
for i in WindTur.name),
name='PwtMax')
mod.addConstrs(
(PGen[t, i] <= PG2Dict[t, i] for t in Time.serie for i in Gen.name),
name='PG2Max')
mod.addConstrs(
(QGen[t, i] <= QG2Dict[t, i] for t in Time.serie for i in Gen.name),
name='QG2Max')
mod.addConstrs((PCoGen[t, i] <= PC1Dict[t, i] for t in Time.serie
for i in CoGen.name),
name='PC1Max')
mod.addConstrs((QCoGen[t, i] <= QC1Dict[t, i] for t in Time.serie
for i in CoGen.name),
name='QC1Max')
mod.addConstrs(( PhoArr.pf[i] * PPhoArr[t,i] == QPhoArr[t,i] \
for t in Time.serie for i in PhoArr.name ), name='PVpf')
mod.addConstrs(( WindTur.pf[i] * PWindTur[t,i] == QWindTur[t,i] \
for t in Time.serie for i in WindTur.name ), name='WTpf')
# Branch flow model
mod.addConstrs(( Pinje[t,j]/ElecSys.baseMVA == Pflow.sum(t,j,'*')/ElecSys.baseMVA - \
Pflow.sum(t,'*',j)/ElecSys.baseMVA + BranCur.prod(appendTime(ElecSys.Zr),t,'*',j) \
for t in Time.serie for j in ElecSys.bus ), name='BranPFlow')
mod.addConstrs(( Qinje[t,j]/ElecSys.baseMVA == Qflow.sum(t,j,'*')/ElecSys.baseMVA - \
Qflow.sum(t,'*',j)/ElecSys.baseMVA + BranCur.prod(appendTime(ElecSys.Zx),t,'*',j) \
for t in Time.serie for j in ElecSys.bus ), name='BranQFlow')
mod.addConstrs(( Vol[t,j] == Vol[t,i] - 2*(ElecSys.Zr[i,j]*Pflow[t,i,j]/ElecSys.baseMVA+ElecSys.Zx[i,j]*Qflow[t,i,j]/ElecSys.baseMVA) + \
(ElecSys.Zr[i,j]**2+ElecSys.Zx[i,j]**2)*BranCur[t,i,j] \
for t in Time.serie for (i,j) in ElecSys.branch ), name='VolEqu')
mod.addConstrs(( Pflow[t,i,j]*Pflow[t,i,j] + Qflow[t,i,j]*Qflow[t,i,j] <= ElecSys.baseMVA**2*Vol[t,i]*BranCur[t,i,j] \
for t in Time.serie for (i,j) in ElecSys.branch ), name='RelaxBranFlow')