[Bldg-sim] Estimating system matrix A from simulation engine

Bryan Eisenhower bryane at engr.ucsb.edu
Wed Oct 31 17:24:40 PDT 2012


Deuk-Woo,

I have thought of this a lot before and will outline my experience 
below, in summary, if you are looking for accurate dynamical systems 
matrices from a building energy model (other than a hand-built RC 
network model), you will probably want to learn *Modelica*. Folks in the 
Modelica community have been using this method to study dynamics and 
controls for over a decade in the automotive, aerospace, and other 
industries.

As for other simulation environments, its really up to the one you 
pick.  Remember that the equations in an energy model are an 
approximation to reality.  The numerical solution of these equations are 
yet another approximation to the dynamics in the equations.  So, if you 
are going to do system identification on the model, you are going to get 
artifacts of both approximations.  In my experience, the numerical 
solvers in programs like E+ and TRNSYS are not developed for accuracy in 
dynamics that you would need for this approach.  They are developed more 
for long term analysis and numerical stability - both of which they do a 
great job on.

I have been involved with a project to try and obtain ABCD matrices from 
*TRNSYS*.  In this project, we went into the fortran code and wrote 
extra code to perturb state variables to observe how they relax and 
obtain matrices from this.  We were successful in implementing this but 
did not trust the results because we felt the solver was overwriting the 
short term dynamics in the equations.

I also worked on ABCD matrices using *EnergyPlus*, this time using a 
different approach.  In this approach, I wrote an analytical model that 
can 'talk' to the EnergyPlus input file and .sql database files.  In the 
sql file, there is most of the information about materials (e.g. 
capacitance), as well as all the bookkeeping on view factors and which 
constructions pertain to which zones.  I wrote some scripts that read 
this file and automatically generate a linearized model.  The linearized 
model does not take any time trace information (it does take some 
operating point information).  It was a lot of work and although I trust 
the results, I wouldn't pass on the code to anyone else because it was a 
bit of a mess in the end. I have published this work this year and if 
you would like the papers, please write me personally.

A fourth data point: *IDA-ICE* is another modeling tool that has a nice 
solver should capture short term dynamics.  I asked Per Sahlin at IBPSA 
London this September if there was a way to produce ABCD matrices from 
the model and he said his customers were not interested (my paraphrasing 
- hopefully correct) - which is completely fair.  My understanding is 
that the historical intersection of control analysis and building energy 
models has been on longer time scales (e.g. setback / setpoint analysis) 
or just time trace analysis - very little stability, frequency domain, 
or other advanced traditional techniques.

Good luck!  Since I have thought of this for some time, I'd be 
interested to discuss further with you, especially if you obtain any 
good results.

Bryan



On 10/30/2012 6:32 PM, 김덕우 wrote:
>
> Thank you for your reply.
>
> Unfortunately, I’m not familiar with Modelica simulation environments.
>
> If you don’t mind, could you please let me know any other ways?
>
> Best Regards,
> Deuk-Woo Kim
>
> *From:*Michael Wetter [mailto:mwetter at lbl.gov]
> *Sent:* Wednesday, October 31, 2012 1:49 AM
> *To:* 김덕우
> *Cc:* bldg-sim at lists.onebuilding.org
> *Subject:* Re: [Bldg-sim] Estimating system matrix A from simulation 
> engine
>
> Most Modelica simulation environments allow you to linearize a model 
> at the current state and save the A,B,C and D matrix that are its 
> state-space representation at the point of linearization. See
>
> Michael Wetter.
>
> Modelica-based Modeling and Simulation to Support Research and 
> Development in Building Energy and Control Systems. 
> <http://dx.doi.org/10.1080/19401490902818259>
>
> /Journal of Building Performance Simulation/, 2(2):143-161, 2009.
>
> Also available as LBNL Technical Report LBNL-2740E.pdf 
> <http://simulationresearch.lbl.gov/wetter/download/LBNL-2740E.pdf>.
>
> where this is demonstrated for a nonlinear heat exchanger model. The 
> Modelica Buildings library 
> (http://simulationresearch.lbl.gov/modelica/) contains a room model 
> which you should be able to use for the same process to get the A,B,C 
> and D matrices for a building model.
>
> Best,
>
> Michael
>
> On Sun, Oct 28, 2012 at 6:54 AM, 김덕우<deukwookim at skku.edu 
> <mailto:deukwookim at skku.edu>> wrote:
>
> Dear all,
>
> Is there a method to estimate system matrix *A* (of zone or building) 
> from simulation engines such as E+, ESP-r??
>
> (The*A* is commonly found in state-space equation, e.g. x’ = *A*x + Bu.)
>
> As far as I know, only system identification method can be applied in 
> this situation.
>
> (but, I not sure that it is reliable)
>
> If there is more advanced way or efficient way to estimate *A, *please 
> let me know.
>
> Any comments would be appreciated.
>
> Thanks in advance.
>
> Best Regards,
> Deuk-Woo Kim
>
>
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