Constraints in a loop in the PowerModels

Specific Domains Optimization (Mathematical)
1

I want to enforce linear envelopes on the cosine function in PowerModelsAnnex. I implement the following code for doing that.

for (bp, buspair) in ref[:buspairs]
for k=1:length(linear_envelopes1)
@constraint(model, cs[bp]>= linear_envelopes1 [k]*td[bp]+ linear_envelopes2 [k])
end
end

I get the following error. Can you please let me know how I can fix this. Thanks in advance!

ERROR: LoadError: The operators <=, >=, and == can only be used to specify scalar constraints. If you are trying to add a vectorized constraint, use the element-wise dot comparison operators (.<=, .>=, or .==) instead

2

Some, or all of your components are vectors. Try the .>= as the error message suggests.

3

Thanks for the response! I have already tried that but I got the following error. I think it is better to define a dictionary for the linear envelope’s coefficient and then used the vectorized constraints.

ERROR: LoadError: MethodError: no method matching addVectorizedConstraint(::JuMP.Model, ::JuMP.GenericRangeConstraint{JuMP.GenericAffExpr{Float64,JuMP.Variable}})
Closest candidates are:
addVectorizedConstraint(::JuMP.Model, ::Array{JuMP.GenericRangeConstraint{JuMP.GenericAffExpr{Float64,JuMP.Variable}},N} where N) at C:\Users\Rasoul.julia\v0.6\JuMP\src\affexpr.jl:221
addVectorizedConstraint(::JuMP.Model, ::Array{JuMP.GenericQuadConstraint{JuMP.GenericQuadExpr{Float64,JuMP.Variable}},N} where N) at C:\Users\Rasoul.julia\v0.6\JuMP\src\quadexpr.jl:172

4

You should read the first post of Please read: make it easier to help you - #11. It’s easier to help if you can provide a minimal working example. What are cs[bp], linear_envelopes1[k], td[pb], and linear_envelopes2[k]?

However, it looks like you are using an old and outdated version of Julia/JuMP. You should update to Julia 1.0 and JuMP 0.21.

5

At first glance it looks like this code should work. So it should be mostly a debugging exercise along the lines @odow has suggested.

Concerning this code,

One thing that stood out to me was that linear_envelopes1 is not indexed first by bp. I would have exepected something like,

for (bp, buspair) in ref[:buspairs]
  for k=1:length(linear_envelopes1[bp])
    @constraint(model, cs[bp]>= linear_envelopes1[bp][k]*td[bp] + linear_envelopes2[bp][k])
  end
end

As I would expect each buspair to have its own envelope. You might be considering a case where there is only one envelope shared across all buspairs. In that case, what you originally proposed was along the right lines.

6

Thanks for the instructive response. In my code each buspair has its own linear envelopes. I have two options to implement the code, I can define a dictionary or I can define a two-dimensional array. Which one do you think is better in terms of execution time?

7

The set of bus pairs is very sparse, so I would recommend Dict(bp => Array[line1, line2, ... n]). The PWL cost function implementation gives an example of this. For example see, PowerModels.jl/objective.jl at v0.15.5 · lanl-ansi/PowerModels.jl · GitHub

8

Thank you so much for the instructive response. It was really helpful!

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