1) The marginal cost is positive. Multiplied by a negative quantity results in
a negative total cost. Increasing the load (negative injection) decreases the
overall objective function. So the load will be fully dispatched, unless the
LMP drops below it’s marginal cost.
2) I’m not sure I completely understand what you’ve done, but you certainly
model this as a generator with negative PMIN and positive PMAX, with a
piecewise linear cost function that passes through the origin. It must be
convex, with increasing slopes for the segments as you go from most negative to
most positive injection.
3) The negative total “cost” associated with the dispatchable load is actually
just the negative of the total benefit derived by the load from it’s
consumption. That’s how we define this cost. So, minimizing the sum of this
(dispatchable load) cost and the generation cost is the same as maximizing the
total benefit to consumers minus the total cost to producers, that is
maximizing the net benefits to society, also called social welfare.
Hope this answers your questions,
Ray
> On Feb 3, 2015, at 2:42 PM, mohd <mansour1...@hotmail.com> wrote:
>
> Dear all,
>
> I would like to understand several points about modeling dispatchable load in
> matpower. I have read section 6.4.2 and i would like to understand how the
> dispatchable load works in the context of its modelling.
>
> 1) If we have negative power injection with a negative cost. My understanding
> is that it will show at the end as a net added cost since we are multiplying
> two negatives?! In this case, i assume, if we want to dispatch a load, it has
> to have a cost that is cheaper than the current cost of operating the most
> expensive generator or at least cheaper than the set LMP price at its
> location. I would like to ensure proper understanding or more clarification
> about that. If my understanding is wrong, then i have an issue of why not
> running all dispatchable load since they will reduce the total cost of the
> system. They are negative!
>
>
> 2) If i model a demand-responding facility that has both a load and
> generation. Based on the price, it will bid either negative or positive
> injection. Positive mean net export to the system and negative means net
> import from the system. What is the best way of modelling that? What i did
> is that, i had my own profit maximization algorithm for the facility that
> provides the net injected power at each price, so i can create my bid
> function. From that, i have started from the highest expected price and
> calculated the associated cost by multiplying my power by the price. So, for
> each change in power, i calculated a change in cost as explained, then i
> started from the highest price to calculate the cumulative power and
> cumulative cost to create the total cost function for the load. In this case,
> how should this be handled when the net injection is positive? I do believe
> that i should not use a negative cost anymore. I need someone to comment on
> my method to ensure i am not making assumptions that are different from
> matpower assumptions for modeling. My curve for the negative injection (load)
> is convex so far but the positive injection is still confusing to me using
> dispatchable load assumption.
>
> 3) The last paragraph in that section states that " it should be noted that,
> with the definition of dispatchable loads as negative generators, if the
> negative cost corresponds to a benefit for consumption, minimizing the cost
> f(x) of generation is equivalent to maximizing social welfare". What do that
> statement mean? does it mean minimizing negative cost means maximizing total
> benefit which social welfare or is it just using the definition of social
> welfare which is worth minus cost and minimizing cost means maximizing SW.
>
> Thanks for your time and effort in trying to answer my questions and
> clarifying the points raised.
>
> Kindly,
> Mans
