Dynamic Programming, MILP, MINLP as well as CVX, Matlab tools etc. are very used for energy flow optimization in microgrids and smart grids.
In my works I can approximate battery non linearity (i.e. charging and discharging efficiencies) through Dynamic Programming.
How can I do the same in CVX?
In particular, how can I implement this equation:
SoC[k]=SoC[k-1]+(Ech[k]*0.95)+(Edch[k]/0.95)
where 0.95 is the battery efficiency in both charging and discharging modes.
Considering that Ech and Edch are complementary variables, namely if one is different to 0 the other must be kept equal to 0 at the same time slot (i.e. k in formula).
Dear Stefano Leonori,
I think R. Bellman's Optimality Principle (Dynamic Programming, DP) is ideal for optimizing energy optimization processes.
With DP you can graphically illustrate the individual steps of the optimization process - i.e. the possible combinations (actual state, next step) - in two-dimensional space (x, y). This is very helpful in solving various tasks. Various optimization problems can be graphically illustrated when using DP.
In my chapter (written in 1972) you will find various simple examples of using DP. The text is in Polish, but the procedure for DP is very clear from the graphics.
https://www.researchgate.net/publication/312033832_Dynamic_Programming
See also my answer at:
https://www.researchgate.net/post/How_can_I_calculate_an_using_energy_of_WSN_node
Best regards and much success
Anatol Badach
Dear Anatol Badach,
Thank you for your useful advices.
I already implemented a DP tool for energy flow optimization.
In this paper I compared a Rolling Time Horizon Strategy based EMS with a Mamdani Fuzzy Inference System EMS optimized with a Genetic Algorithm
Article Optimization strategies for Microgrid energy management syst...
For this work, I used the DP tool of prof. Guzzella from the University of Salerno.
My point is to use a faster optimization algorithm, indeed DP is very time consuming. Moreover, it works on a discretized space, hence the solution found is not optimal.
Currently, I'm trying to use the "fmincon" function of matlab. It seems it's working, however i'm not convinced.
For example, it is necessary to distinguish the energy bought and sell from the grid as well as the energy charging and discharging of the battery.
These are nonlinearities that I think make the optimization problem non convex.
Stefano
I hope that these papers can help you
Article Economic Dispatch of Renewable Generators and BESS in DC Mic...
Article Economic dispatch of energy storage systems in dc microgrids...
HI Stefano!
Have you solved this problem?
I have the solution to it by the way.
Dear Ehtisham,
I found some two solutions but I still have to work on it.
The first is to formulate a MILP which consider TH binary variables where TH is the time horizon length (e.g. a T.H. of 1 day defined by 24 time slot means TH=24).
However, this solution does not allow the implementation of some objective functions. For example i can not minimize the energy oscillations given by the energy exchanged with the grid that in my opinion is very important.
It would allo the flatten the energy exchange with the grid, namely
1) minimization (E^N[k])^2-(E^N[k-1])^2 for each time slot (for further information about the objective function see [1])
2) The implementation of Time Of Use or Dynamic energy prices without considering any constraint on the ESS energy exchange sign seems not possible (To do this I applied a trick in [2]).
Another solution is to use a intlinprog in Matlab, that should allow to impllement 1), not sure for 2) without special constraints.
What is your idea?
[1] An optimized microgrid energy management system based on FIS-MO-GA paradigm, July 2017, DOI:10.1109/FUZZ-IEEE.2017.8015438,Conference: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
[2] Optimization strategies for Microgrid energy management systems by Genetic Algorithms, DOI: 10.1016/j.asoc.2019.105903
Sorry for late reply, you can see my paper in this I used CVX to do this kind of work.
Stefano Leonori
Sure please use the below link and let me know if you need any information.
https://www.sciencedirect.com/science/article/pii/S0306261918318889
I recently published on Applied Energy a paper about prosumer energy management systems where I discuss the limits of Rolling Time Horizon (Model Predictive Control) based models.
If you are interested, here below you can find the link
Article Microgrid Energy Management Systems Design by Computational ...
Stefano
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