Defining ppriority and pwidth of ALLOCATE AVAILABLE function

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WayneZhou2009
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Defining ppriority and pwidth of ALLOCATE AVAILABLE function

Post by WayneZhou2009 »

Hi Tomfid and Administrator,

I have a question about defining the ppriority and pwidth of the ALLOCATE AVAILABLE function. Suppose I have 2 types of power plants to construct to meet an increasing power demand (exogenous).

- For Plant A, its average capital cost is 1000 USD/KW and standard deviation is 200 USD/kW. Assuming that I only care capital cost and ignore O&M and fuel costs, so I use -1000 for ppriority and 200 for pwidth.

- For Plant B, its average capital cost is 1500 USD/KW and standard deviation is 400 USD/kW. Assuming that I only care capital cost and ignore O&M and fuel costs, so I use -1500 for ppriority and 400 for pwidth.

For both, ptype is 3, i.e. normal distribution. Based on the above defined priority profiles, and assuming the available capacities/resources to construct both types are much higher than the power demand, ALLOCATE AVAILABLE can produce the installed capacities of both types over time.

The above is based purely on cost consideration. Now, I also want to take plant efficiency into consideration when defining the priority profiles. Suppose plant A's efficiency is 30%, whereas plant B's efficiency is 50%, then apparently the efficiency levels have an impact on the prioritization.

My question is how could the efficiency be "integrated" with the cost consideration in the definition of priority profile of ALLOCATE AVAILABLE function?

I understand this may sound like an optimization problem for which each a VECTOR LOOKUP or a closed-form solution could solve, as Tomfid kindly advised in my previous post (http://www.ventanasystems.co.uk/forum/v ... f=2&t=6873 ). But the issue here is that the capital cost is a range, rather than a single number. So how should priority (or, attractiveness) be formulated in such a situation? Would something like the following equation still make sense in the context of ALLOCATE AVAILABLE function? How to deal with the standard deviation then?

Plant A ppriority = EXP((Average capital cost of plant A / Reference capital cost)*Cost Sensitivity ) * EXP((Efficiency of plant A / Reference efficiency)*Efficiency Sensitivity )


Thank you so much.
tomfid
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Re: Defining ppriority and pwidth of ALLOCATE AVAILABLE function

Post by tomfid »

As a general approach, treating multiple attributes in the priority expression as essentially a multiplicative or exponential utility function makes sense.

However, in this particular case, I think you'd want to account for why efficiency matters. No one really cares about efficiency per se; they're interested because it affects operating cost, and maybe other things, like emissions.

So, in a situation like this, I'd combine the expected costs of capital, fuel (modified by efficiency), O&M, and emissions (fuel / efficiency * emissions intensity * shadow price of pollutant) into a single levelized cost. Then use that to drive the priority.
WayneZhou2009
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Re: Defining ppriority and pwidth of ALLOCATE AVAILABLE function

Post by WayneZhou2009 »

Hi Tomfid,

Many thanks for your reply. Yes, the plant efficiency is of concern because of emissions. So, if I understand your suggested approach correctly, that would lead to a combined "ppriority" under priority profile of the ALLOCATE AVAILABLE function which is sort of "fixed"? In other words, as long as the shadow price of emissions is fixed, then the overall priority profile of a given type of plant, measured using the single levelized cost, would remain unchanged?

However, what I want to find out is the way of making the priority profile of a given type of plant "dynamic". That is to say, during the course of meeting the power demand, I want to not only control my costs, but also total emissions. In extreme situations, I would only construct plant A if all I care is money, or I would only construct plant B if all I care is efficiency (thus emissions). But now I have to balance both.

So I guess the priority profile should be "dynamic" over time? Suppose I can work out a levelized cost of electricity generation (LCOE) which does not cover emissions, and also suppose NO shadow price for emissions exist. So, for each plant type, it's priority profile is measured through two indicators, which are (1) the LCOE (dollar/kWh) and (2) the emission factor ( kgCO2/kWh). Over time, the weightage of LCOE relative to the weightage of emission factor in the priority profile of a plant should vary, meaning that for example in early years priority profile of plant A is more sensitive to LCOE and later on it is made more sensitive to emission factor. Something like that.

If this is sensible, then how to realise it through ALLOCATE AVAILABLE? As the emissions are not monetized, can I combine the two indicators as follows, and use it as the ppriority in the ALLOCATE AVAILABLE function? In this equation, the sensitivities are variable rather than fixed, so as to be dynamic.

Plant A ppriority = EXP((LCOE of plant A / Reference LCOE )*Cost Sensitivity ) * EXP((Emission factor of plant A / Reference emission factor)*Emission Factor Sensitivity )

If the above makes sense, how should pwidth be defined appropriately?

Thanks so much!

tomfid wrote:As a general approach, treating multiple attributes in the priority expression as essentially a multiplicative or exponential utility function makes sense.

However, in this particular case, I think you'd want to account for why efficiency matters. No one really cares about efficiency per se; they're interested because it affects operating cost, and maybe other things, like emissions.

So, in a situation like this, I'd combine the expected costs of capital, fuel (modified by efficiency), O&M, and emissions (fuel / efficiency * emissions intensity * shadow price of pollutant) into a single levelized cost. Then use that to drive the priority.
WayneZhou2009
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Posts: 105
Joined: Wed Oct 25, 2017 3:52 pm
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Re: Defining ppriority and pwidth of ALLOCATE AVAILABLE function

Post by WayneZhou2009 »

Hi Tomfid / Administrator,

I am not sure if you have got a chance to read my questions above, but I would be very grateful if you could offer some comments/advices.

A related question is that: suppose cost is the only criterion to determine priority of plants, but for each plant type, the cost is a curve (say, normal distribution), rather than a single point estimate. Then, how could exponential utility function be used to treat the priority expression? In other words, in the equation of Share of plant type A = exp (utility A) / (exp (utility A) + exp (utility B) + exp (utility C) +...), how should the cost be appropriately translated to utility, given that the cost for each plant type is a range? Furthermore, I think this equation appears to be a multinomial logit model (MNL).

Would ALLOCATE AVAILABLE function be the only way to enable the treatment of priority curve in such a situation?

Many thanks for your time!
tomfid
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Re: Defining ppriority and pwidth of ALLOCATE AVAILABLE function

Post by tomfid »

Many thanks for your reply. Yes, the plant efficiency is of concern because of emissions. So, if I understand your suggested approach correctly, that would lead to a combined "ppriority" under priority profile of the ALLOCATE AVAILABLE function which is sort of "fixed"? In other words, as long as the shadow price of emissions is fixed, then the overall priority profile of a given type of plant, measured using the single levelized cost, would remain unchanged?

However, what I want to find out is the way of making the priority profile of a given type of plant "dynamic". That is to say, during the course of meeting the power demand, I want to not only control my costs, but also total emissions. In extreme situations, I would only construct plant A if all I care is money, or I would only construct plant B if all I care is efficiency (thus emissions). But now I have to balance both.
I think you need dynamic priorities if shares are to be dynamic.
So I guess the priority profile should be "dynamic" over time? Suppose I can work out a levelized cost of electricity generation (LCOE) which does not cover emissions, and also suppose NO shadow price for emissions exist. So, for each plant type, it's priority profile is measured through two indicators, which are (1) the LCOE (dollar/kWh) and (2) the emission factor ( kgCO2/kWh). Over time, the weightage of LCOE relative to the weightage of emission factor in the priority profile of a plant should vary, meaning that for example in early years priority profile of plant A is more sensitive to LCOE and later on it is made more sensitive to emission factor. Something like that.
I don't see any way of getting around the fact that any weight you put on emissions relative to LCOE is a de facto emissions price, i.e. it converts kgCO2 to $. There might be situations where you want a constraint on emissions rather than a price, but even then there will always be a shadow price that is equivalent to the constraint. The constraint might make the shadow price volatile or zero at times, but it's still there. I think there's actually an insight for decision makers here: quantity constraints on emissions have bad properties. Environmental taxes or fees behave much better. However, you'll get a lot of resistance to that idea.

http://metasd.com/2010/03/painting-ours ... en-corner/
http://metasd.com/2009/03/ethanol-odd-c ... rnia-lcfs/
http://metasd.com/2010/03/lcfs-in-equilibrium-ii/
http://metasd.com/2008/11/news-flash-th ... certainty/
If this is sensible, then how to realise it through ALLOCATE AVAILABLE? As the emissions are not monetized, can I combine the two indicators as follows, and use it as the ppriority in the ALLOCATE AVAILABLE function? In this equation, the sensitivities are variable rather than fixed, so as to be dynamic.
Again, I think you have no choice but to monetize emissions, at least implicitly. The combination of Cost Sensitivity and Emission Factor Sensitivity below amounts to a price.
Plant A ppriority = EXP((LCOE of plant A / Reference LCOE )*Cost Sensitivity ) * EXP((Emission factor of plant A / Reference emission factor)*Emission Factor Sensitivity )

If the above makes sense, how should pwidth be defined appropriately?
The answer here depends a bit on what shape you're using. If it's exponential or normal, I think you don't need the EXP around the terms. You might simply sum LCOE and emissions x shadow price, and use the net price as a priority. Then the pwidth should be chosen to reflect the diversity of plant conditions in operation. For example, if you're using the Normal shape, it would literally be the standard deviation of levelized costs of plants of a given type.
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