# Variables for power flow with condition in constraint
**URL:** https://discourse.julialang.org/t/variables-for-power-flow-with-condition-in-constraint/116343
**Category:** Optimization (Mathematical)
**Tags:** question, jump, power-flow
**Created:** [June 28, 2024, 8:58am UTC](https://discourse.julialang.org/t/variables-for-power-flow-with-condition-in-constraint/116343 "2024-06-28T08:58:53Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@priantop](https://discourse.julialang.org/u/priantop)
#### Post date: [June 28, 2024, 8:58am UTC](https://discourse.julialang.org/t/variables-for-power-flow-with-condition-in-constraint/116343/1 "2024-06-28T08:58:54Z")
Hi,
I am formulating LP problem using JuMP for electricity dispatch
below is the MWE
I have variables for power flow and export/import to neighbouring regions defined as follows
```julia
using JuMP, HiGHS
m = Model(HiGHS.Optimizer)
buses = 1:5
trade_buses = 2:3
hours = 1:24
# power flow
@variable(m, P[i in buses, j in buses, t in hours ; i != j])
# export/import to region
@variable(m, X[i in trade_buses , t in hours])
@variable(m, gen[i in buses, t in hours] >= 0)
@variable(m, totalcost) # objective
```
those variables are unbounded since my logic is that when P\>0, P flows from i to j, else P flows from j to i.
Same logic for X, X\>0 means exporting to other regions, otherwise importing.
then I define the following constraints and objective
```julia
#hypothetical data
demand = 10 .+ (50-10) .* rand(length(buses), length(hours))
fuelcost = 0.2
tradecost = 1 .+ (100-1) .* rand(length(hours))
# bus balance
@constraint(m, balance[i in buses, j in buses, t in hours ; i != j],
demand[i, t] + P[i, j, t] +
(i in trade_buses ? X[i, t] : 0) <= gen[i, t]
)
# export/import to region
@constraint(m, cost,
totalcost == sum(gen[i, t] * fuelcost for i in buses, t in hours) +
sum(i in trade_buses && X < 0 ? X[i, t] * tradecost[t] : 0 for i in buses, t in hours)
)
```
for constraint cost, I only want the trade cost only incurred when i is in trade\_bus and when it is importing (i.e. X \< 0)
but it throws this error
> ERROR: MethodError: no method matching isless(::JuMP.Containers.DenseAxisArray{VariableRef, 2, Tuple{UnitRange{Int64}, UnitRange{Int64}}, Tuple{JuMP.Containers.\_AxisLookup{Tuple{Int64, Int64}}, JuMP.Containers.\_AxisLookup{Tuple{Int64, Int64}}}}, ::Int64)
> Closest candidates are:
> isless(::Missing, ::Any)
> @ Base missing.jl:87
> isless(::Any, ::Missing)
> @ Base missing.jl:88
> isless(::ForwardDiff.Dual{Tx}, ::Integer) where Tx
> @ ForwardDiff C:\Users\prianto.julia\packages\ForwardDiff\PcZ48\src\dual.jl:144
> …
the following are my questions:
1. Is condition for the variables within constraint is not allowed?
2. or my syntaxing is incorrect and there is a better way?
3. or should i split the trade variable into export and import, when cost only incurred to the import?
4. if splitting into two variables is the way to go, should i apply the same for the P variable? e.g. Pfrom will be P from bus i, Pto will be P to bus i. This is in case later on I would incur cost of power flow.
Sorry if the question is too long!
Thank you very much in advance!
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [June 29, 2024, 12:02am UTC](https://discourse.julialang.org/t/variables-for-power-flow-with-condition-in-constraint/116343/2 "2024-06-29T00:02:47Z")
> [@priantop](#):
>
> Is condition for the variables within constraint is not allowed?
It is not allowed.
The error message is not good because you have `X < 0`. Did you mean instead `X[i, t] < 0`? I think if you had done that you’d get a nicer error message.
For your other questions, yes, you need to model `X = X_plus - X_neg` where `X_plus` and `X_neg` are both `>= 0`. You’ll end up with a formulation that allows simultaneous flows in both directions, which is a known problem with this sort of LP formulation.
If you’re solving power flow problems, you should look up (if you haven’t already)
- [GitHub - lanl-ansi/PowerModels.jl: A Julia/JuMP Package for Power Network Optimization](https://github.com/lanl-ansi/PowerModels.jl)
- [PowerModelsAnnex.jl/src/model/dc-opf.jl at master · lanl-ansi/PowerModelsAnnex.jl · GitHub](https://github.com/lanl-ansi/PowerModelsAnnex.jl/blob/master/src/model/dc-opf.jl)
---
### Author:  [@priantop](https://discourse.julialang.org/u/priantop)
#### Post date: [June 29, 2024, 4:42am UTC](https://discourse.julialang.org/t/variables-for-power-flow-with-condition-in-constraint/116343/3 "2024-06-29T04:42:58Z")
> [@odow](#):
>
> > I think if you had done that you’d get a nicer error message.
Ah yes I completely missed that, now it gives this error, which is understandable
```julia
ERROR: TypeError: non-boolean (NonlinearExpr) used in boolean context
```
> [@odow](#):
>
> If you’re solving power flow problems, you should look up (if you haven’t already)
Thanks for the suggestion @odow! Will look into these!
I looked into JuMP Optimal Power Flow tutorial previously and did not find similar branch flow formulations there