Model changing lifetime due to renovation

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WayneZhou2009
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Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi,

I am trying to model a situation where X% of every year's elements of an aging chain undergo renovation and therefore have increased lifetime (and as a result, will be scrapped at times later than originally expected). More specifically, suppose I have a stock of 1000 newly developed power generation plants and their lifetime follows a normal distribution, with average lifetime of 50 years and standard deviation of 15 years. These 1000 power generation plants age every year. The development of these plants are assumed to be realised within one single year, modelled using PULSE at year 0. Their aging process is modelled using subscripting. Hence, stock of plants [t] represents the stock of plants that remain operational t years after the development. Because of the scrappage of old plants reaching the end of their lifetime every year, stock of plants [t] decreases over time. The scrappage curve follows a normal distribution, i.e. the lifetime distribution.

Now, what I am struggling with is that: in any given year t, if X% percentage of the plants that remain operational (i.e. stock of plants [t] ) are renovated for extending their remaining lifetime, then the overall scrappage curve (lifetime distribution) of the entire stock of plants will be changed. This is because those renovated plants will stay in the stock for longer period before they finally leave the stock (scrapped). For simplicity, I assume that a single renovation will extend a plant's remaining lifetime by 10 years as a fixed amount. I also assume that the percentage X% per year is known, although it varies per year, say, 0.2% for 1st year, 0.3% for 2nd year, and so on. However, the remaining lifetime for those X% plants renovated per year is unknown - some of them might have 5 years remaining lifetime, some might have 35 years, and so on, but they will all have lifetime extension by 10 years after renovation.

In such a situation, I want to know the plants that remain operational per year (i.e. stock of plants [t] ). I cannot find a way to properly "spread" those increased remaining lifetime of renovated plants in a year over the aging chain following that year.

Could someone point me in the right direction please? Many thanks.
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Re: Model changing lifetime due to renovation

Post by Administrator »

I'm finding it hard to follow what you are asking without an example.

But it does sound like a "re-work" structure to me. And I know there are examples of this on the web.
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Thanks. However I feel that the issue is different from re-work. I have attached a simple example for review and discussion. For simplicity, I did not use subscript. Some comments are written in the model for explaining the issue.

Many thanks.
Administrator wrote:I'm finding it hard to follow what you are asking without an example.

But it does sound like a "re-work" structure to me. And I know there are examples of this on the web.
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Impact of renovation on lifetime.mdl
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tomfid
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Re: Model changing lifetime due to renovation

Post by tomfid »

Do you need discrete plants, or can you have fractional retirement and refitting?
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi Tomfid, I am not sure if I fully understand your question. No, it is not required that the plants must be discrete, because the total number is very big. Fraction is okay. Could you please offer some advice on how to solve it? Many thanks.
tomfid wrote:Do you need discrete plants, or can you have fractional retirement and refitting?
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Re: Model changing lifetime due to renovation

Post by tomfid »

That's the answer I was looking for.

I think what you need is essentially an aging chain for plants. The question is how many levels you need to get the right amount of dispersion in retirements. My delay sandbox, http://metasd.com/2011/04/delay-sandbox/, has some thoughts on this. For example, if you break the 50yr life up into 5yr stages, the normalized sd is about 30%, or the 15yrs you mention. So, that might be about right - if a bit inconvenient.

For retrofits, you could reinject them into the aging chain according to their new remaining life - so perhaps they leave from the 40-year-old box and arrive in the 20-year-old box.

Another option would be to keep track of plant cohorts, i.e. organize them by the nameplate year (or decade) in which they were constructed. That reduces the dispersion problem, so it might be easier to get the desired sd without a lot of levels. On the other hand, you need some empty cohorts in advance (or use Ventity).

You could also make retirement an economic decision, and track plant performance (heat rate, maintenance cost) as a coflow of the number of plants. Then plants retire, not because they're old, but because they're inefficient or unreliable. That has the added virtue of making the lifetime variable - if coal gets really cheap, the coal plants are kept online longer, for example. Retrofits would not make plants younger, but would make them perform better, and therefore less prone to retirement. However, you'd still need the aging chain or cohorts alongside this.
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi Tom,

Thank you so much. In fact, I did use an aging chain for the plants. The aging chain is based on subscripting. Each cohort of plants has a duration of 1 year. The solution interval is also 1 year. This is to prevent blending. So, there are a total of 100 cohorts of plants. Mapping of subscripts is used to model the aging from cohort to cohort [i+1]. The subscript ranges from 0 to 100, representing plant age. ( I did not use subscripting in the uploaded model for simplicity purpose.)

I had considered to set the retrofit flow of a cohort as the inflow of a younger cohort on the aging chain, namely, the "reinjection" as you suggested. So, assuming retrofit can increase a plant's remaining lifetime by 20 years, then the reinjection flow is the retrofitted plants leaving cohort and entering cohort [i-20]. However, my questions are:

(1) Can this "reinjection" be a treatment reasonably equivalent to somehow spreading the increased remaining lifetime of retrofitted plants over those older cohorts on the chain, i.e. "backward" vs "forward"?

(2) Suppose the reinjection is the proper method, I found it difficult to integrate the reinjection flow into the aging chain. The mapping of subscripts seems to be difficult. For cohort [0] to cohort [19], their retrofit flow will be re-injected to nowhere because there are no cohorts 20 years YOUNGER than them (no negative cohort index). For cohort [81] to cohort [100], they will have no reinjection flow to receive because there no cohorts 20 years OLDER than them on the chain (the cohort index is capped at 100). So, the mapping seems only possible for the following subranges?

Reinjection: (0 - 80)
Retrofit flow: (20 - 100) -> Reinjection

(3) Moreover, how could this mapping be aligned with the original mapping used to enable the aging chain which use the mapping of something like ALL BUT OLDEST -> ALL BUT YOUNGEST ?

Thank you so much for your further thoughts.

tomfid wrote:That's the answer I was looking for.

I think what you need is essentially an aging chain for plants. The question is how many levels you need to get the right amount of dispersion in retirements. My delay sandbox, http://metasd.com/2011/04/delay-sandbox/, has some thoughts on this. For example, if you break the 50yr life up into 5yr stages, the normalized sd is about 30%, or the 15yrs you mention. So, that might be about right - if a bit inconvenient.

For retrofits, you could reinject them into the aging chain according to their new remaining life - so perhaps they leave from the 40-year-old box and arrive in the 20-year-old box.

Another option would be to keep track of plant cohorts, i.e. organize them by the nameplate year (or decade) in which they were constructed. That reduces the dispersion problem, so it might be easier to get the desired sd without a lot of levels. On the other hand, you need some empty cohorts in advance (or use Ventity).

You could also make retirement an economic decision, and track plant performance (heat rate, maintenance cost) as a coflow of the number of plants. Then plants retire, not because they're old, but because they're inefficient or unreliable. That has the added virtue of making the lifetime variable - if coal gets really cheap, the coal plants are kept online longer, for example. Retrofits would not make plants younger, but would make them perform better, and therefore less prone to retirement. However, you'd still need the aging chain or cohorts alongside this.
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Re: Model changing lifetime due to renovation

Post by Administrator »

Maybe mapping is not the way to do it here (I've always struggled with subscript mapping myself).

I've attached a model that does what I think you need. I haven't implemented the ageing chain, just the retrofit.
plant_retrofit.mdl
(3.03 KiB) Downloaded 228 times
The constant "additional years plants get when retrofitted" is the number of extra lifetime years that a plant gets on retrofit (10 years in this example). From this, I calculate the age bucket that a retrofitted plant will drop into ("age retrofitted plants drop to"). And using this, I loop over all age buckets and sum only those that should fall into the bucket being calculated ("retrofitted plants rate").

If you look at the tabular output, you'll see that all "plants to retrofit" from ages 1-11 drop back to "age 1", age 12 drops to age 2, etc.

It's really important when doing complex mapping and moving things between levels to implement a mass balance check (MBC). If you are not familiar with them, all you do is sum up what is in the system (including what has been added/removed), you should always have a constant. If the MBC varies, then you are either double accounting or losing things from your stocks.
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi Administrator,

Many thanks for the model and your explanation. It provides an interesting perspective other than mapping subscripts. For the "retrofitted plants rate", why does "plants to retrofit [age]" need to be summed over age? Also, after including all subscript elements into the simulation (i.e. including a21 to a100), the graph of "retrofitted plants rate" appears to be weird, if the line for [a1] is hidden and the others are zoomed in, it can be seen that many lines intertwine together. Is this the reasonable behaviour? Or perhaps I have misunderstood the fundamental logic behind this model.

Administrator wrote:Maybe mapping is not the way to do it here (I've always struggled with subscript mapping myself).

I've attached a model that does what I think you need. I haven't implemented the ageing chain, just the retrofit.
plant_retrofit.mdl

The constant "additional years plants get when retrofitted" is the number of extra lifetime years that a plant gets on retrofit (10 years in this example). From this, I calculate the age bucket that a retrofitted plant will drop into ("age retrofitted plants drop to"). And using this, I loop over all age buckets and sum only those that should fall into the bucket being calculated ("retrofitted plants rate").

If you look at the tabular output, you'll see that all "plants to retrofit" from ages 1-11 drop back to "age 1", age 12 drops to age 2, etc.

It's really important when doing complex mapping and moving things between levels to implement a mass balance check (MBC). If you are not familiar with them, all you do is sum up what is in the system (including what has been added/removed), you should always have a constant. If the MBC varies, then you are either double accounting or losing things from your stocks.
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Re: Model changing lifetime due to renovation

Post by Administrator »

WayneZhou2009 wrote:why does "plants to retrofit [age]" need to be summed over age?
The "sum" is actually looping over the age subscript and only getting those that re-enter at the relevant age.
WayneZhou2009 wrote:Also, after including all subscript elements into the simulation (i.e. including a21 to a100), the graph of "retrofitted plants rate" appears to be weird, if the line for [a1] is hidden and the others are zoomed in, it can be seen that many lines intertwine together. Is this the reasonable behaviour? Or perhaps I have misunderstood the fundamental logic behind this model.
Ignore the graphs/numbers, I made the numbers up just to test the structure.
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WayneZhou2009
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi Administrator, thanks for further explanation. So, for those plants aged between 1 and 10, their extra lifetime years gained through a retrofit are less than 10 years? For example, for a plant aged 7, after retrofit, its age will drop to 1, which means the extra lifetime gained is 6 years. Is this a correct interpretation of your model? And also, does this structure imply the possibility that a plant retrofitted at year T might get retrofitted again in the immediately next year T+1?

Just one additional question, why is the function INITIAL necessary in the equation for "age retrofitted plants drop to"?

Many thanks for your time.
Administrator wrote:
WayneZhou2009 wrote:why does "plants to retrofit [age]" need to be summed over age?
The "sum" is actually looping over the age subscript and only getting those that re-enter at the relevant age.
WayneZhou2009 wrote:Also, after including all subscript elements into the simulation (i.e. including a21 to a100), the graph of "retrofitted plants rate" appears to be weird, if the line for [a1] is hidden and the others are zoomed in, it can be seen that many lines intertwine together. Is this the reasonable behaviour? Or perhaps I have misunderstood the fundamental logic behind this model.
Ignore the graphs/numbers, I made the numbers up just to test the structure.
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Re: Model changing lifetime due to renovation

Post by Administrator »

WayneZhou2009 wrote:So, for those plants aged between 1 and 10, their extra lifetime years gained through a retrofit are less than 10 years? For example, for a plant aged 7, after retrofit, its age will drop to 1, which means the extra lifetime gained is 6 years
Correct.
WayneZhou2009 wrote:And also, does this structure imply the possibility that a plant retrofitted at year T might get retrofitted again in the immediately next year T+1?
It's possible in my model. But this is just to demonstrate how to move things from one subscript range to another, it's not supposed to be an accurate model (or any kind of model, it's just demonstrating how to move subscripts).
WayneZhou2009 wrote:Just one additional question, why is the function INITIAL necessary in the equation for "age retrofitted plants drop to"?
It's not necessary. I use INITIAL if the calculation only needs to be done once.
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Re: Model changing lifetime due to renovation

Post by tomfid »

I think the same thing could be implemented with VECTOR ELM MAP, which would be efficient because it avoids the loop over ages.

However, I'm questioning the idea of reinjecting plants to an earlier age slot. Can they be renovated again as they age further? How many times? How would you keep track?
WayneZhou2009
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi Tom, thanks for your comments. Yes, that bothers me, too. Reinjection would mean that a certain plant is likely to be renovated again sometime soon, which does not make sense in real life. One way round it is to perhaps set a certain time period (e.g. 5 years, 10 years, or so) during which the already renovated plant will not be renovated. Alternatively, perhaps some probability distribution could be applied to control the frequency/likelihood of a plant undergoing 2nd, 3rd, 4th renovations in the future. But, as you pointed out, how to track a certain plant is the issue. I have not come up with ideas about how to translate these thoughts into Vensim models... Any advices would be greatly appreciated.

tomfid wrote:I think the same thing could be implemented with VECTOR ELM MAP, which would be efficient because it avoids the loop over ages.

However, I'm questioning the idea of reinjecting plants to an earlier age slot. Can they be renovated again as they age further? How many times? How would you keep track?
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Re: Model changing lifetime due to renovation

Post by LAUJJL »

Hi

This problem is difficult to solve partly because the purpose of modelling this problem is not known. What do you expect from this model?

Reading the thread I could not find the purpose.

To resume what will be the model useful for?

Regards.

JJ
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi JJ, thanks for your comments. The purpose of the modelling is to study the trend of average efficiency of the power plants ( measured in the unit of gram coal consumed per kWh generated). There is a natural improvement of the efficiency over time, as a result of technological advancement. Moreover, it is considered that retrofitting a power plant will lead to not only a certain percentage of efficiency improvement, but also an increase of its remaining life (say, 10 years).

Hence, as previously discussed, the challenge is how to model the increase of lifetime upon a retrofit. One possible way is to reinject a retrofitted plant in cohort [age] to cohort [age -10]. This means the retrofitted plant needs to be taken out from its current age cohort, and injected into the age cohort 10 years younger than it. (Does this really make sense??!!) But the issue is that there is the possibility that a plant retrofitted at year T might get retrofitted again in the immediately next year T+1, a scenario which is highly unlikely in reality.

Another possible way might be to somehow "spread" the increased remaining lifetime of a retrofitted plant over those older cohorts on the aging chain, so as to have some impact on the scrappage profile. This is the opposite way to the reinjection. However, I am clueless about how to realize this in the model.

I would be grateful if you could offer some suggestions.
LAUJJL wrote:Hi

This problem is difficult to solve partly because the purpose of modelling this problem is not known. What do you expect from this model?

Reading the thread I could not find the purpose.

To resume what will be the model useful for?

Regards.

JJ
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Re: Model changing lifetime due to renovation

Post by tomfid »

You might take a look at the energy consuming capital with efficiency coflows in this model:
http://metasd.com/2010/03/the-energy-tr ... e-economy/

It seems to me that there are multiple states of potential interest:
- age
- time since retrofit/upgrade
- efficiency
- original efficiency

I think it makes sense to have an explicit aging chain or cohort structure, so no question there. It also makes sense to track efficiency, and maybe original efficiency, as a coflow (as in the Sterman model).

So, the big question is retrofits. I see 3 options using conventional SD:
- track "fraction of plants retrofitted" as a coflow, like efficiency
- reinject retrofits from later periods into younger age groups
- maintain a separate, parallel aging chain for retrofitted plants (avoiding the immediate re-retrofit problem, but creating new problems for multiple retrofits)

Getting away from SD a bit, you might be able to use the QUEUE functions to manage things, as long as you can tolerate the assumption that plants retire in strict age order.

Failing that, I think you need essentially a discrete event or agent approach, with an array of individual plants making discrete state transitions. This might actually be easier to set up, if you don't mind the extra run time.
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi Tom, many thanks for your further comments. I totally agree with you on the need of using aging chain and also co-flow, which are what I have already used. The headache is the retrofit - more specifically, the extra lifetime due to each retrofit.

Regarding the reinjection: for a cohort of plants at a certain age (say, 30 years old), the expected situation is this cohort receives reinjection of retrofitted plants aged 40, and also "loses" its retrofitted portion because its retrofitted portion is reinjected to the 20-year-old cohort. However, there is the 10 year gap between the loss and the reinjection, meaning that at year 30 the 30-year-old cohort lose its retrofitted portion and then only at year 30+10 it will receive the reinjection of retrofitted 40-year-old cohort. This is because the reinjection is not available at year 30 - it only happens at year 30+10. The loss and gain do not happen simultaneously. So, when plants get old and the stock of plants in use is low due to massive scrappage, the loss of retrofitted plants makes old cohorts negative, and such negative status remains 10 years until the loss is offset by reinjection to some extent. This does not seem to make practical sense - the retrofitted plants remain physically there. Moreover, simply changing the tags of a cohort, from its current age to age-10, does not seem to make a difference to its remaining lifetime. Something has to be done to change its scrappage rate/probability after retrofit?

For tracking the fraction of plants retrofitted as the 1st option, I fail to understand how this will address the extra lifetime issue. Pls could you elaborate a bit further?

Similarly, for maintaining a separate parallel aging chain for retrofitted plants, I do not think this will address the extra lifetime. Unless the scrappage profile (lifetime distribution) is manually re-set, say, by increasing the original average lifetime of 50 years to increased average lifetime of 60 years. And this increased average lifetime applies to those retrofitted plants. Is this what you implied? However, multiple retrofits cannot be solved in this option, unless the number of retrofits is arbitrarily decided ex-ante.
tomfid wrote:You might take a look at the energy consuming capital with efficiency coflows in this model:
http://metasd.com/2010/03/the-energy-tr ... e-economy/

It seems to me that there are multiple states of potential interest:
- age
- time since retrofit/upgrade
- efficiency
- original efficiency

I think it makes sense to have an explicit aging chain or cohort structure, so no question there. It also makes sense to track efficiency, and maybe original efficiency, as a coflow (as in the Sterman model).

So, the big question is retrofits. I see 3 options using conventional SD:
- track "fraction of plants retrofitted" as a coflow, like efficiency
- reinject retrofits from later periods into younger age groups
- maintain a separate, parallel aging chain for retrofitted plants (avoiding the immediate re-retrofit problem, but creating new problems for multiple retrofits)

Getting away from SD a bit, you might be able to use the QUEUE functions to manage things, as long as you can tolerate the assumption that plants retire in strict age order.

Failing that, I think you need essentially a discrete event or agent approach, with an array of individual plants making discrete state transitions. This might actually be easier to set up, if you don't mind the extra run time.
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Re: Model changing lifetime due to renovation

Post by LAUJJL »

Hi

To solve that problem, I would start with a very simple model that I have understood fully by using it.

This problem needs an ageing chain with multiple co-flows to trace different attributes as Tom mentioned.

I would then build an ageing chain of 5 cohorts of plants based on their life time expectancy and not on their real age. The first cohort with have an average life time expectancy 45, the second of 35 etc.. in the case of a delay fixed and the flow between the cohorts could be modelled by a delay fixed or a simple flow equal to the level/average time in the level. Things to be tested.

I would first build with that a co-flow of the number of retrofitted actions already performed and still in use (not the retrofitted plants) performed within each of the cohort, that will permit to trace how much in average in a cohort the plants have been already retrofitted. And I would study that model extensively to understand the fundamental problem: how works the retrofitting. For instance if in the cohort 30-40 30 plants are retrofitted, they will be re injected in the 20-30 cohort (if the retrofit adds 10 years to the expected life time) and 30 retrofits will be added to the level 20-30 of the number of retrofits performed co-flow.

Of course both chains have to be managed as the time is passing on.

It is possible to start working with two cohorts instead of 5. The simpler a model the better.

Apart from that it is difficult to give an advice on a subject that one has little information to work with. On top of that I have never worked on this type of problems, which makes my advices to be considered with care and no guarantee.

Regards.

JJ
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi JJ,

Many thanks for sharing your thoughts. I do not fully understand your suggestion that "build an ageing chain of 5 cohorts of plants based on their life time expectancy and not on their real age".

However, I built a simplified model, to highlight the fundamental issue of concern. In the attached model, the aging chain has only 5 cohorts, with each cohort's duration being just 1 year. That means, the 1st cohort is for 1-year-old plants, the 2nd cohort is for 2-year-old plants, and so on. For each cohort, there is certain scrappage. It is assumed that retrofit happens to the 3rd, 4th and 5th cohorts, but not the 1st and 2nd ones. The oldest cohort is 5 years old.

Each retrofit leads to lifetime increase by 2 years. Hence, the retrofitted plants in the 3-year-old cohort, 4-year-old cohort and 5-year-old cohort are reinjected into the 1-year-old cohort, 2-year-old cohort, and 3-year-old cohort, respectively. The retrofit fraction is 10% of the relevant cohorts.

The results seem to indicate the reinjection works, to some extent. The increase of retrofit fraction from 0 to 10%, 20%, 30% and so on, does lead to more plants (sum of all ages) remaining in use after year 6. However, when the fraction increases to a high level, the 4-year-old cohort shows some negative values. Perhaps I have done something wrong?

Could you elaborate a bit further on the idea of making the retrofit fraction a co-flow? I found it unclear to implement, as I think retrofit fraction is of a different nature from efficiency, which is an attribute associated with each and every plant.

Thank you so much.

LAUJJL wrote:Hi

To solve that problem, I would start with a very simple model that I have understood fully by using it.

This problem needs an ageing chain with multiple co-flows to trace different attributes as Tom mentioned.

I would then build an ageing chain of 5 cohorts of plants based on their life time expectancy and not on their real age. The first cohort with have an average life time expectancy 45, the second of 35 etc.. in the case of a delay fixed and the flow between the cohorts could be modelled by a delay fixed or a simple flow equal to the level/average time in the level. Things to be tested.

I would first build with that a co-flow of the number of retrofitted actions already performed and still in use (not the retrofitted plants) performed within each of the cohort, that will permit to trace how much in average in a cohort the plants have been already retrofitted. And I would study that model extensively to understand the fundamental problem: how works the retrofitting. For instance if in the cohort 30-40 30 plants are retrofitted, they will be re injected in the 20-30 cohort (if the retrofit adds 10 years to the expected life time) and 30 retrofits will be added to the level 20-30 of the number of retrofits performed co-flow.

Of course both chains have to be managed as the time is passing on.

It is possible to start working with two cohorts instead of 5. The simpler a model the better.

Apart from that it is difficult to give an advice on a subject that one has little information to work with. On top of that I have never worked on this type of problems, which makes my advices to be considered with care and no guarantee.

Regards.

JJ
Attachments
Retrofit reinjection.mdl
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LAUJJL
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Re: Model changing lifetime due to renovation

Post by LAUJJL »

Hi

I have made some corrections to your model.

First correction, error units, I have changed some parameters from DMNL to 1/year.

Another problem is the capacity to draw more from a level that its value and the level becomes negative. This becomes from the formulation of the reinjection that does not take into account any preliminary scrapping.

In fact one must describe precisely how things work.

At the beginning of the year, the manager decides how many plants to scrap. Or he may decide how many plants to retrofit first, but I decide to apply the first option that looks more credible.
Once this scrapping decision is taken, he decides how many of the plants still there to retrofit.
The level is then equal to level at the beginning of the year minus the scrapping, minus the retrofitting that is equal to (beginning level – scrapping) * percentage of retrofitting. He then adds what comes from the preceding level and what is eventually retrofitted from a following level and after that the ageing is done. In your formulation things are not very clear and there are possible errors if the time step is reduced or in the case of larger cohorts with larger cohort duration.

If one applies this strict process, there is less risk of error, things being clear.

Joined a model with the corrections.

I will build later a model based on the expected life instead of the age, that to my opinion may be easier to manage.

I do not see clearly what can be done with this one, having not idea of how many retrofits have been already made by plant.

I do not guarantee that there are not still errors or errors of mine in the model joined that must be used and tested eventually with a mass balance.

Joined with the model a run with 100 plants built each year, that stabilizes Under 500 hundred plans at 440, which looks credible


Regards.

JJ
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Retrofit reinjection_corrected.vpm
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tomfid
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Re: Model changing lifetime due to renovation

Post by tomfid »

Another possible approach - borrowing the cohort style from Ventity:
retrofit 1.mdl
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WayneZhou2009
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi JJ,

Thank you so much for making corrections and explaining your thoughts. Subtracting the scrap from the level in order to calculate the reinjection helps solve the problem of negative values. The logic behind it, as you explained, makes sense. I am expanding this model by putting up co-flows to test whether it returns reasonable results.

Yes, as you said, the problem is that it is not possible to know how many retrofits have been performed. And it does not seem to avoid the situation where a retrofitted plant is retrofitted again in the immediately next year. This is the "con". However, the "pro" is that this method (reinjection) seems to enable multiple retrofits.

I look forward very much to seeing your model based on the expected life instead of age.

Thanks a lot.
LAUJJL wrote:Hi

I have made some corrections to your model.

First correction, error units, I have changed some parameters from DMNL to 1/year.

Another problem is the capacity to draw more from a level that its value and the level becomes negative. This becomes from the formulation of the reinjection that does not take into account any preliminary scrapping.

In fact one must describe precisely how things work.

At the beginning of the year, the manager decides how many plants to scrap. Or he may decide how many plants to retrofit first, but I decide to apply the first option that looks more credible.
Once this scrapping decision is taken, he decides how many of the plants still there to retrofit.
The level is then equal to level at the beginning of the year minus the scrapping, minus the retrofitting that is equal to (beginning level – scrapping) * percentage of retrofitting. He then adds what comes from the preceding level and what is eventually retrofitted from a following level and after that the ageing is done. In your formulation things are not very clear and there are possible errors if the time step is reduced or in the case of larger cohorts with larger cohort duration.

If one applies this strict process, there is less risk of error, things being clear.

Joined a model with the corrections.

I will build later a model based on the expected life instead of the age, that to my opinion may be easier to manage.

I do not see clearly what can be done with this one, having not idea of how many retrofits have been already made by plant.

I do not guarantee that there are not still errors or errors of mine in the model joined that must be used and tested eventually with a mass balance.

Joined with the model a run with 100 plants built each year, that stabilizes Under 500 hundred plans at 440, which looks credible


Regards.

JJ
WayneZhou2009
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Re: Model changing lifetime due to renovation

Post by WayneZhou2009 »

Hi Tom,

Thank you so much for sharing this interesting model. The treatment of "Cohort Start" and "Cohort Age" appears to be important. Still trying to understand the INITIAL equations for Cohort Start - appreciate if you could elaborate a bit.

If I understand it correctly, this model avoids the immediate re-retrofit problem, but does not enable multiple retrofits?

tomfid wrote:Another possible approach - borrowing the cohort style from Ventity:
retrofit 1.mdl
tomfid
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Re: Model changing lifetime due to renovation

Post by tomfid »

The idea here is to avoid some hassles - in exchange for a little more compute time - by having static cohorts rather than an aging chain. So, nothing has to move as it ages - it just ages in place.

So, "cohort start" is the time the cohort is "born," i.e. at which new construction starts filling it. The age is then the time elapsed since the start. Initially, there are ten existing cohorts, populated with stylized data. Then there have to be enough new cohorts to cover the time horizon of the model.

It would be very easy to add a second retrofit here by adding one more stock to the chain. There are probably other ways to do it (as for a regular aging chain), but not if you want to strictly avoid the re-retrofit problem.
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