Please help me with my optimal power flow problem

varun_yaramasu
Mon, 18 Nov 2019 07:16:09 +0000
General Usage

using JuMP,Ipopt

m=Model(with_optimizer(Ipopt.Optimizer))

from to r x b Max_MVA(rate)

branch=[ 1 2 0.1 0.2 0.04 60
1 4 0.05 0.2 0.04 90
1 5 0.08 0.3 0.06 50
2 3 0.05 0.25 0.06 40
2 4 0.05 0.1 0.02 70
2 5 0.1 0.3 0.04 50
2 6 0.07 0.2 0.05 50
3 5 0.12 0.26 0.05 50
3 6 0.02 0.1 0.02 80
4 5 0.2 0.4 0.08 30
5 6 0.1 0.3 0.06 30
];

bus bus type Pd Qd Pg Qg theta

bus=[ 1 3 0 0 110 0 0
2 2 0 0 80 0 0
3 2 0 0 50 0 0
4 1 50 10 0 0 0
5 1 100 15 0 0 0
6 1 100 15 0 0 0
];

n_b=length(bus[:,1])
ng=3;#generation buses+slack bus
nl=3;#load buses

Ybus =[ 4.0063-11.7479im -2.0000+4.0000im 0.0000+0.0000im -1.1765+4.7059im -0.8299+3.1120im 0.0000+0.0000im
-2.0000+4.0000im 9.3283-23.1955im -0.7692+3.8462im -4.0000+8.0000im -1.0000+3.0000im -1.5590+4.4543im
0.0000+0.0000im -0.7692+3.8462im 4.1557-16.5673im 0.0000+0.0000im -1.4634+3.1707im -1.9231+9.6154im
-1.1765+4.7059im -4.0000+8.0000im 0.0000+0.0000im 6.1765-14.6359im -1.0000+2.0000im 0.0000+0.0000im
-0.8299+3.1120im -1.0000+3.0000im -1.4634+3.1707im -1.0000+2.0000im 5.2933-14.1378im -1.0000+3.0000im
0.0000+0.0000im -1.5590+4.4543im -1.9231+9.6154im 0.0000+0.0000im -1.0000+3.0000im 4.4821-17.0047im
]

@variable(m,PG[1:ng])
@variable(m,QG[1:ng])
@variable(m,theta[1:(n_b-1)])
@variable(m,V[1:n_b])

#D=250
α=[30.0053 30.00889 30.00741]
β=[311.669 310.333 310.833]
γ=[3213.1 3200 3*240]

P_min=[50 37.5 45]’
P_max=[200 150 180]’

Q_min=[-100 -100 -100]’
Q_max=[150 150 120]’

V_min=[0.9 0.9 0.9 0.9 0.9 0.9]’
V_max=[1.1 1.1 1.1 1.1 1.1 1.1]’

theta_min=[-20 -20 -20 -20 -20]‘*pi/180
theta_max=[20 20 20 20 20]’*pi/180

LB=[theta_min; V_min; P_min; Q_min]
UB=[theta_max; V_max; P_max; Q_max]

Pg=[PG[1] PG[2] PG[3] 0 0 0]‘/100
Qg=[QG[1] QG[2] QG[3] 0 0 0]’/100
Pd=[0 0 0 50 100 100]‘/100 #%Active Power demand at each bus
Qd=[0 0 0 10 15 15]’/100 #%Reactive Power demand at each bus

P=Pg-Pd #Active power calculated at ith bus
Q=Qg-Qd # Reactive power calculated ith bus

@variable(m,Paux)
@constraint(m,Paux .==P)

@variable(m,Qaux)
@constraint(m,Qaux .==Q)

theta=[0;theta]

function V_bus(V,theta)
V.exp(theta1im)
end

function S_bus(V_bus,Ybus)
V_bus(V,theta).*(conj(Ybus.*V_bus(V,theta)))
end

function P_bus(S_bus)
real(S_bus(V_bus(V,theta),Ybus))
end

function Q_bus(S_bus)
imag(S_bus(V_bus(V,theta),Ybus))
end

@objective(m,Min,sum(α[i]*PG[i]^2+β[i]*PG[i]+γ[i] for i in 1:3))

@constraint(m,Paux-P_bus(S_bus(V_bus(V,theta),Ybus)) ==0)
@constraint(m,Qaux-Q_bus(S_bus(V_bus(V,theta),Ybus)) ==0)

@constraint(m,theta[1:5] .<=UB[1:5])
@constraint(m,theta[1:5] .>=LB[1:5])

@constraint(m,V[1:n_b] .<=UB[6:11])
@constraint(m,V[1:n_b] .>=LB[6:11])

@constraint(m,PG[1:ng] .<=UB[12:14])
@constraint(m,PG[1:ng] .>=LB[12:14])

@constraint(m,QG[1:ng] .<=UB[15:17])
@constraint(m,QG[1:ng] .>=LB[15:17])

println(“The optimization problem to be solved is:”)
print(m)
JuMP.optimize!(m)
optimvalue=JuMP.objective_value(m)
PG=JuMP.value.(PG)
QG=JuMP.value.(QG)
V=JuMP.value.(V)
theta=JuMP.value.(theta)

println(“Objective value:”,optimvalue)
println(“PG1=:”,PG[1])
println(“PG2=:”,PG[2])
println(“PG3=:”,PG[3])

println(“QG1=:”,QG[1])
println(“QG2=:”,QG[2])
println(“QG3=:”,QG[3])

println(“V1=:”,V[1])
println(“V2=:”,V[2])
println(“V3=:”,V[3])
println(“V4=:”,V[4])
println(“V5=:”,V[5])
println(“V6=:”,V[6])

println(“theta2=:”,theta[1])
println(“theta3=:”,theta[2])
println(“theta4=:”,theta[3])
println(“theta5=:”,theta[4])
println(“theta6=:”,theta[5])

#PG3=JuMP.value(PG[i] for i in 3)
#PG2=JuMP.value(PG[i])
#PG3=JuMP.value(PG3)

#println(“PG2=:”,PG2)
#println(“PG3=:”,PG3)

3 posts - 2 participants