In 2 stage stochastic optimization, why I found that the optimization problem has equations for the 1st stage and equations for the 2nd stage but those two groups are solved simultaneously however I think that we first solve the 1st stage equations then take the results and substitute in the 2nd stage equations (new problem) or there is something I overlooked?
Also why we dont combine the equations for 1st and 2nd stages as they are solved simultaneously ?
my case study is for power systems with renewable energy uncertainty when I make day ahead decisions for the power dispatch, power dispatch of each generator are computed (1st stage decisions) then after the realization of uncertain events (renewable energy) redispatch is done in the 2nd stage using reserve or may some load shedding is done.
My question is how the decisions of the 2 stages done simultaneously as I see from some papers. why we optimize the 1st stage first and run our optimization then take the results and apply them in the 2nd stage problem and run it again? and if the optimization of the 2 stages made simultaneously, why we did not combine the equations (constraints) of the 2 stages together ? as I see 1st stage constraints and 2nd stage constraints.
I have an interesting industrial case study for you... When you see a truck loaded with tanks of oxygen or nitrogen, know that these come from a gas separation plant. We start with air, cool it until it becomes a liquid, then run it through a fractional distillation column to split it into the components, which have different vaporization points. Operators adjust the controls to get the most product. Humans only adjust one control at a time, sequentially. I was able with software to adjust multiple settings at the same time, each one individually non-optimal, but combined better than any one. The output of the plant went up by 3.5%, while the power consumption went up by only 1.5%, for a net 2% improvement. This might not sound like much until you see that it means 20 tons of O2 per day! Complex multi-dimensional nonlinear optimization problems can be challenging to solve but just might yield results that would pay your salary for the rest of your life and make you a very valuable employee!
Dudley J Benton thanks for your reply but my case study is for power systems with renewable energy uncertainty when I make day ahead decisions for the power dispatch, power dispatch of each generator are computed (1st stage decisions) then after the realization of uncertain events (renewable energy) redispatch is done in the 2nd stage or may some load shedding is done.
My question is how the decisions of the 2 stages done simultaneously as I see from some papers. why we optimize the 1st stage first and run our optimization then take the results and apply them in the 2nd stage problem and run it again?
I agree that both decisions should be considered together. I know of several large power producers that do just that. I wrote the original scheduling software for several of TVA's plants and more that was used at the Load Control Center. I have performed many historical simulations of this sort and recently published a book on the subject (https://www.amazon.com/dp/B07YJ1JFLS ) The book will be free on the Tuesday after Christmas. The software (including several plant models) is free here http://dudleybenton.altervista.org/software/index.html More of the power plant models can be seen here http://dudleybenton.altervista.org/projects/Power%20Plants/PowerPlants.html Appendix A of the book has a whole list of links to publications you can download free with a description of each. Appendices B, C, and D explain how to get weather data for anywhere on Earth and build that into the model. I have provided spreadsheet models for several plants that go out and grab the latest weather predictions, estimate the capacity for multiple units, factor in the ramp rates and demand, then calculate the advantage of bringing units up or down, switching from simple cycle to combined cycle, and turning duct firing on or off, including how this might impact their emissions quotas. Of course, these last are proprietary, but I'd be glad to get you started building your own.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Energy
- Energy-Generating Resources
- Renewable Energy