Dear Ray,
Thanks for the clarification. Note my comments and questions in sequence:
1) When i derived it as injections in the objective function, the picture
became more clear to me. The only thing to note is that you are assuming lambda
to be always positive. In some markets with subsidies, the price could go
negative as in ERCOT with the current level of wind penetration. One question
that might arise is how to deal with negative price in modelling! This means a
positive cost again. If so, how can i make the shift such that the curve still
maintains its convexity.
2) I have a facility that has both a load as well as its internal generation.
My derivation shows convexity which is the main assumption for optimization.
However, i was asking how to model the load when it has both positive and
negative injections, especially during the shift from load to generation. What
i did is that since my load bids around 500 MW for a low price close to zero,
i ended the point as (-500,0), then i made a straight line (flat) till point
(0,0). After that, i started the generation side from (0,0) and made my next
point, all using the piece wise cost curve and using the break points listed. I
hope my approach is correct and i am sorry for not explaining myself well in
the first e-mail.
3) I got the point but i wanted to make sure it is not related to the modelling
assumption for dispatchable load. I am used to other terms such as worth, cost,
and social welfare but thanks for the information.
I hope that you can comment on my points, especially point-2. Thanks and take
care.
Kindly,Mans
From: r...@cornell.edu
Subject: Re: Dealing with dispatchable loads
Date: Wed, 4 Feb 2015 13:47:41 -0500
To: matpowe...@list.cornell.edu
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
