Optimization Methods in Energy and Power Systems Lecture
![Optimization Methods in Energy and Power Systems Lecture 11: Stochastic Programming Mahdi Pourakbari Kasmaei, Optimization Methods in Energy and Power Systems Lecture 11: Stochastic Programming Mahdi Pourakbari Kasmaei,](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-1.jpg)
![Stochastic Programming ü Introduction of Stochastic Programming ü Stochastic Process ü Stochastic Programming • Stochastic Programming ü Introduction of Stochastic Programming ü Stochastic Process ü Stochastic Programming •](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-2.jpg)
![Stochastic Programming (Quality Metrics) ü Quality Metrics are used to reveal the interest of Stochastic Programming (Quality Metrics) ü Quality Metrics are used to reveal the interest of](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-3.jpg)
![Stochastic Programming (Quality Metrics: EVPI) ü Expected Value of Perfect Information (EVPI) demonstrates the Stochastic Programming (Quality Metrics: EVPI) ü Expected Value of Perfect Information (EVPI) demonstrates the](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-4.jpg)
![Stochastic Programming (Quality Metrics: EVPI) ü For EVPI calculations, the scenario-variable model is used. Stochastic Programming (Quality Metrics: EVPI) ü For EVPI calculations, the scenario-variable model is used.](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-5.jpg)
![Stochastic Programming (Quality Metrics: EVPI) Example 11. 1: Obtain the EVPI for the two-stage Stochastic Programming (Quality Metrics: EVPI) Example 11. 1: Obtain the EVPI for the two-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-6.jpg)
![Stochastic Programming (Quality Metrics: EVPI) Example 11. 2: Obtain the EVPI for the three-stage Stochastic Programming (Quality Metrics: EVPI) Example 11. 2: Obtain the EVPI for the three-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-7.jpg)
![Stochastic Programming (Quality Metrics: VSS) ü Value of Stochastic Solution (VSS) is used to Stochastic Programming (Quality Metrics: VSS) ü Value of Stochastic Solution (VSS) is used to](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-8.jpg)
![Stochastic Programming (Quality Metrics: VSS) ü For EVPI calculations, the following steps are considered. Stochastic Programming (Quality Metrics: VSS) ü For EVPI calculations, the following steps are considered.](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-9.jpg)
![Stochastic Programming (Quality Metrics: VSS) Example 11. 3: Obtain the VSS for the two-stage Stochastic Programming (Quality Metrics: VSS) Example 11. 3: Obtain the VSS for the two-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-10.jpg)
![Stochastic Programming (Quality Metrics: VSS) Example 11. 4: Obtain the VSS for the three-stage Stochastic Programming (Quality Metrics: VSS) Example 11. 4: Obtain the VSS for the three-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-11.jpg)
![Thanks! M. Pourakbari Kasmaei, 2019 12 Thanks! M. Pourakbari Kasmaei, 2019 12](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-12.jpg)
- Slides: 12
![Optimization Methods in Energy and Power Systems Lecture 11 Stochastic Programming Mahdi Pourakbari Kasmaei Optimization Methods in Energy and Power Systems Lecture 11: Stochastic Programming Mahdi Pourakbari Kasmaei,](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-1.jpg)
Optimization Methods in Energy and Power Systems Lecture 11: Stochastic Programming Mahdi Pourakbari Kasmaei, 2019 Thursday, 16 May 2019
![Stochastic Programming ü Introduction of Stochastic Programming ü Stochastic Process ü Stochastic Programming Stochastic Programming ü Introduction of Stochastic Programming ü Stochastic Process ü Stochastic Programming •](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-2.jpg)
Stochastic Programming ü Introduction of Stochastic Programming ü Stochastic Process ü Stochastic Programming • Two- and Multi-Stage Problems ü Quality Metrics M. Pourakbari Kasmaei, 2019 2
![Stochastic Programming Quality Metrics ü Quality Metrics are used to reveal the interest of Stochastic Programming (Quality Metrics) ü Quality Metrics are used to reveal the interest of](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-3.jpg)
Stochastic Programming (Quality Metrics) ü Quality Metrics are used to reveal the interest of applying stochastic programming. • Deterministic problems are obtained out of stochastic programming by fixing the random variable to an expected or forecaste values ü Two main metrics are: • Expected Value of Perfect Information (EVPI) • Value of the Stochastic Solution (VSS) M. Pourakbari Kasmaei, 2019 3
![Stochastic Programming Quality Metrics EVPI ü Expected Value of Perfect Information EVPI demonstrates the Stochastic Programming (Quality Metrics: EVPI) ü Expected Value of Perfect Information (EVPI) demonstrates the](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-4.jpg)
Stochastic Programming (Quality Metrics: EVPI) ü Expected Value of Perfect Information (EVPI) demonstrates the price that a decision maker is willing to pay for obtaining perfect information about the future. ü Let us assume a two-sage stochastic programming Model. The EVPI for Maximization and Minimization Problems are calculated as follows. PI and S stand for Perfect information-, and Stochasticbased models, respectively. M. Pourakbari Kasmaei, 2019 4
![Stochastic Programming Quality Metrics EVPI ü For EVPI calculations the scenariovariable model is used Stochastic Programming (Quality Metrics: EVPI) ü For EVPI calculations, the scenario-variable model is used.](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-5.jpg)
Stochastic Programming (Quality Metrics: EVPI) ü For EVPI calculations, the scenario-variable model is used. ü The calculations are done as follows. • Relax the non-anticipativity condition. • Solve the relaxed Problem M. Pourakbari Kasmaei, 2019 5
![Stochastic Programming Quality Metrics EVPI Example 11 1 Obtain the EVPI for the twostage Stochastic Programming (Quality Metrics: EVPI) Example 11. 1: Obtain the EVPI for the two-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-6.jpg)
Stochastic Programming (Quality Metrics: EVPI) Example 11. 1: Obtain the EVPI for the two-stage problem presented in Lecture 9, Ex. 9. 5. Let us solve it together! M. Pourakbari Kasmaei, 2019 6
![Stochastic Programming Quality Metrics EVPI Example 11 2 Obtain the EVPI for the threestage Stochastic Programming (Quality Metrics: EVPI) Example 11. 2: Obtain the EVPI for the three-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-7.jpg)
Stochastic Programming (Quality Metrics: EVPI) Example 11. 2: Obtain the EVPI for the three-stage problem presented in Lecture 10, Ex. 10. 2. Let us solve it together! M. Pourakbari Kasmaei, 2019 7
![Stochastic Programming Quality Metrics VSS ü Value of Stochastic Solution VSS is used to Stochastic Programming (Quality Metrics: VSS) ü Value of Stochastic Solution (VSS) is used to](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-8.jpg)
Stochastic Programming (Quality Metrics: VSS) ü Value of Stochastic Solution (VSS) is used to quantify the advantage of using a stochastic programming over the deterministic one. ü Let us assume a two-sage stochastic programming Model. The VSS for Maximization and Minimization Problems are calculated as follows. D and S stand for Deterministic, and Stochastic models, respectively. M. Pourakbari Kasmaei, 2019 8
![Stochastic Programming Quality Metrics VSS ü For EVPI calculations the following steps are considered Stochastic Programming (Quality Metrics: VSS) ü For EVPI calculations, the following steps are considered.](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-9.jpg)
Stochastic Programming (Quality Metrics: VSS) ü For EVPI calculations, the following steps are considered. • Random variables of the stochastic process are replaced by their respective expected values. • The optimal values for the first-stage variables are obtained. • The original Stochastic problem can then be solved by fixing the values of the first-stage variables (to those provided by the deterministic one). M. Pourakbari Kasmaei, 2019 9
![Stochastic Programming Quality Metrics VSS Example 11 3 Obtain the VSS for the twostage Stochastic Programming (Quality Metrics: VSS) Example 11. 3: Obtain the VSS for the two-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-10.jpg)
Stochastic Programming (Quality Metrics: VSS) Example 11. 3: Obtain the VSS for the two-stage problem presented in Lecture 9, Ex. 9. 4. Let us solve it together! M. Pourakbari Kasmaei, 2019 10
![Stochastic Programming Quality Metrics VSS Example 11 4 Obtain the VSS for the threestage Stochastic Programming (Quality Metrics: VSS) Example 11. 4: Obtain the VSS for the three-stage](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-11.jpg)
Stochastic Programming (Quality Metrics: VSS) Example 11. 4: Obtain the VSS for the three-stage problem presented in Lecture 10, Ex. 10. 1. Let us solve it together! M. Pourakbari Kasmaei, 2019 11
![Thanks M Pourakbari Kasmaei 2019 12 Thanks! M. Pourakbari Kasmaei, 2019 12](https://slidetodoc.com/presentation_image_h2/bfa0c54020f9aa07f43a35e3443ac8e4/image-12.jpg)
Thanks! M. Pourakbari Kasmaei, 2019 12
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