I meant that fp and fn would be per branch, representing the positive (“from”
—> “to”) and “negative” (“to” —> “from”) flow in each branch. The fp – fn will
have to equal the flow in the lines, which can be expressed in terms of the bus
angles (this is the first constraint I suggested).
You can then write a new constraint in terms of the relevant fp and fn elements
to get the constraints you want. For example, suppose the interface in
question, say from area A to area B consists of lines 2, 4 and 6, where the
orientation of lines 2 and 6 have their “from” bus in area A and “to” bus in
area B, and suppose line 4 has the opposite orientation. Then you could
constrain the “positive” and “negative" flows on the interface with constraints
like …
fp(2) + fn(4) + fp(6) <= positive_limit
fn(2) + fp(4) + fn(6) <= negative_limit
Hope this clears up what I had in mind,
Ray
> On May 5, 2015, at 12:01 PM, Hewes, Dominic <[email protected]> wrote:
>
> Hi Ray,
>
> Thanks for your advice. I had not considered using new variables and this is
> a new area for me, so I hope my questions are not too dumb. The process of
> introducing new variables and constraining them makes sense, as do the
> additional constraints that you suggest for fp and fn:
>
> fp – fn = p_i(theta)
> fp >= 0
> fn >= 0
>
> However, I am very unsure as to how I can link the new variables to the
> positive and negative flows. The constraints that you suggested will ensure
> that the sum of the positive and negative flows will equal the total sum of
> the flow between two areas. But I do not understand how can I further
> constrain fp and fn such that fp = sum(positive_flow) and fn =
> sum(negative_flow) using linear constraints.
>
> After looking through some of the existing extensions, I can’t find any
> examples of constraints or variables being applied based on the sign of other
> variables and so I am really not sure of how to implement this. Am I
> overthinking this problem? Any further advice would be very appreciated.
>
> Regards,
>
> Dominic
>
> Von: [email protected]
> <mailto:[email protected]>
> [mailto:[email protected]
> <mailto:[email protected]>] Im Auftrag von Ray
> Zimmerman
> Gesendet: Montag, 4. Mai 2015 19:24
> An: MATPOWER discussion forum
> Betreff: Re: Adaption of Interface Flow Limits Extension
>
> Hi Dominic,
>
> Yes, it can be done, but you will need to introduce some new variables, say
> fp and fn, to represent the positive and negative components of the branch
> flows. Then you can construct the constraints you want on those variables,
> rather than directly on the flows themselves (the p_i from (7.6) in the
> User’s Manual
> <http://www.pserc.cornell.edu/matpower/docs/MATPOWER-manual-5.1.pdf>) as is
> done by the current implementation.
>
> You will need additional constraints to define these new variables, such as …
>
> fp – fn = p_i(theta)
> fp >= 0
> fn >= 0
>
> With zero cost on fp and fn, it’s still possible that both would be positive
> at the same time for flows where your constraints aren’t binding. It
> shouldn’t really affect anything, but if it bothers you, you could add a very
> tiny cost to them.
>
> Ray
>
>
> On May 4, 2015, at 11:21 AM, Hewes, Dominic <[email protected]
> <mailto:[email protected]>> wrote:
>
> Dear Matpower Community,
>
> The ‚Interface Flow Limits‘ extension allows me to limit the sum of all line
> flows between two areas to within a set range. However, I want to instead
> apply two limits – one to the sum of the positive flows, and one to the
> negative flows. For example, whilst the sum of the flow between area 1 and
> area 2 can be set as 1200MW using the existing iflims extension, I want to
> ensure that the flow from area 1 to area 2 = 1400MW and the flow from area 2
> to area 1 = 200MW. My question is the following: is it possible using user
> defined constraints to achieve my aim in matpower?
>
> I would need to apply one constraint to the sum of positive flows from area 1
> to 2, whilst applying another constraint to the sum of negative flows from
> area 1 to 2 – but I cannot work out how to write this as a matpower
> constraint. Any help with this problem would be appreciated.
>
> Regards,
>
> Dom
