Yet another thread on simultaneous equations

[mikdale]

Hi everyone

Can someone please help me. I am trying to model the global energy system but have run into a problem with simultaneous equations.

Essentially I have demand driving the need for energy capital which then is able to extract energy from the environment with some surplus because the energy return on investment (EROI) is greater than one. The amount of energy extracted is dependent on the EROI which is itself a function of the ratio of energy extraction (EE) to the technical potential (TP). I have attached the problematic aspect of the model.

I have tried initialising all of the variables with a value but that hasn't sorted out the problem. I can't use the SIMULTANEOUS function as I have PLE Plus. Can anyone help me with this.

Much appreciated

Mik

[bob@vensim.com]

Capital is a level - in order to increase there must be investment (a rate) and it is decreased by depreciation. Extraction depends on this, not on the capital required. Available nonrenewable energy is also a level, decreased by consumption.

I am attaching a simple depletion model that illustrates this.

[mikdale]

Hi Bob

Thanks for the quick response.

The model that you sent works for depletable resources (non-renewable) and that works fine in my model, but I am also trying to model renewable resources too, where I don't have a level.

I've attached my full model. Any suggestions in this case?

Mik

[bob@vensim.com]

The full model makes a little bit more sense.

If you think about it, the efficiency of extraction depends not on the rate of extraction, but on the amount of stuff in place to allow that extraction. For example, with solar there would be a downward curve as panels are erected in less ideal locations.

To capture this with minimal changes to your model use potential renewable extraction as the input to ratio ARE to TP where

potential renewable extraction = Renewable Capital Stock/lifetime renewable capital

note that this formulation using lifetime renewable capital is very strange. The ability of capital to produce has nothing whatsoever to do with its lifetime. You might want to step back and rethink the formulation and nomenclature used there.

[LAUJJL]

Hi

To push a bit further the advice from Bob to reformulate your problem, I would consider describing with words your problem not forgetting anything. You should take enough time to do it correctly and reread it again to make sure that everything is clear and that somebody else may understand it. If one works alone on a problem there is a strong incentive to forget this critical step and even to jump directly to the quantitative model. I try generally to make a complete description of the problem, then build an influence diagram or causal loop diagram of this definition. If you build a diagram you will discover ambiguities and have a better understanding of the problem. You can even build diagrams with different levels of details to help communicate your ideas and take a higher view of the problem. Once you have done that you can translate your qualitative diagram in a quantitative model that will represent exactly what you described at the beginning with words.
Regards.
JJ

[mikdale]

Hi Bob and JJ

Thanks for the help.

I have thought having the EROI change as a function of the Renewable Capital Stock normalized to the maximum capital stock needed to achieve the full potential extraction, but unfortunately that is exactly what I don't know and partly what I am trying to find out by building the model.

The circularity would be allowed if I had a level in the causal loop. Is there some way that the annual renewable extraction could feed into a level (the value of which is then used by 'fraction of ARE to TP') that then empties before the next time step, i.e. it's value at all time steps is equal to that of annual renewable extraction?

Regards

Mik

[mikdale]

Hi there

I have re-jigged my model to include a level (see attached), so that the value of the level is INTEG((f(t) - f(t-1))/dt), but now I need to feed the value of 'annual renewable extraction' from the previous timestep to the rate leaving the level.

I can't seem to find any means by which to do this. Is it possible? From the notes I can't figure out if the DELAY function passes values from previous time steps or later time steps.

Help would be much appreciated

Mik

[mikdale]

Hi there

I've managed to create a level that matches the value of the flow.

Thanks

Mik

[BrentTylerw]

The full model makes a little bit more sense.

If you think about it, the efficiency of extraction depends not on the rate of extraction, but on the amount of stuff in place to allow that extraction. For example, with solar panels there would be a downward curve as panels are erected in less ideal locations.

To capture this with minimal changes to your model use potential renewable extraction as the input to ratio ARE to TP where

potential renewable extraction = Renewable Capital Stock/lifetime renewable capital

note that this formulation using lifetime renewable capital is very strange. The ability of capital to produce has nothing whatsoever to do with its lifetime. You might want to step back and rethink the formulation and nomenclature used there.

Nice informative post.. I will try your way out and hope for some good outcomes.. Thread is old so sorry for posting.. Will share my experience very soon