Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty †
Abstract
:1. Introduction
- Development and application of a novel robust MPC Method based on zonotopes extending classical tube-based approaches for tackling an uncertain energy dispatch problem in smart micro-grids including several heterogeneous generators and storage elements.
- Assessing the suitability and reliability of Economic MPC paradigm to incorporate the developed robust MPC method.
- The proposed method tackles the effect of demand uncertainty by tightening the system constraints in real-time as the uncertainty propagates throughout the prediction horizon.
2. Problem Statement
2.1. Control-Oriented Modelling
2.2. Control Objectives
2.2.1. Economic Cost
2.2.2. Safety Storage Levels
- -
- Upper safety level:
- -
- Lower safety level:
2.2.3. Smoothness of the Control Actions
2.3. Formulation of the Nominal Economic MPC Controller
3. Robustyfing the MPC Controller
3.1. Decomposition of the Control Variables
3.2. Decomposition of the State Variables
4. Formulation of the Robust MPC
4.1. Open-Loop Approach
4.2. Closed-Loop Approach
5. Application
5.1. Description
5.2. Control-Oriented Model
5.3. Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Model Parameters | Energy Prices (e.u) | ||
---|---|---|---|
0.90 | Lead-acid battery charging: | 0.34 | |
1 | Lead-acid battery discharging: | 0.34 | |
0.90 | Hydrogen battery charging: | 0.34 | |
1.0 | Hydrogen battery discharging: | 0.34 | |
Power flow between node: | 0.34 | ||
External grid selling: | 4.3 | ||
24 | External grid buying: | 4.3 | |
2500 | Diesel: | 8.9 | |
12 | Hydroelectric: | 1.95 | |
0.1 | Wind: | 3.7 | |
Solar: | 3.1 |
Nominal EMPC (Zero Uncertainty) | Robust Closed-Loop EMPC | Robust Open-Loop EMPC | |
---|---|---|---|
Summer | 1125.2 | 1154.4 | 1143.6 |
Winter | 1428.7 | 1448.4 | 1437.1 |
Nominal EMPC (Zero Uncertainty) | Robust Closed-Loop EMPC | Robust Open-Loop EMPC | |
---|---|---|---|
Summer | 1131.7 | 1184.0 | unfeasible |
Winter | 1433.6 | 1466.2 | unfeasible |
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Nassourou, M.; Blesa, J.; Puig, V. Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty. Energies 2020, 13, 696. https://doi.org/10.3390/en13030696
Nassourou M, Blesa J, Puig V. Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty. Energies. 2020; 13(3):696. https://doi.org/10.3390/en13030696
Chicago/Turabian StyleNassourou, Mohamadou, Joaquim Blesa, and Vicenç Puig. 2020. "Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty" Energies 13, no. 3: 696. https://doi.org/10.3390/en13030696