Dynamic Power Management for Portable Hybrid Power-Supply Systems Utilizing Approximate Dynamic Programming
2. Problem Formulation
2.1. System Configuration and Related Background
2.2. State Equation and Performance Index
- In , it is assumed that the charge values of the batteries and supercapacitors take only discrete values. In this study, we omit this assumption; thus, rcap,i(t) and rbat(t) are all real-valued.
- In the model in , supercapacitors are constrained to not be simultaneously charged by the battery and discharged by the load. In this paper, we omit this constraint.
- In the model in , a decision for assigning the source to the workload is carried out such that only one electronic energy supply source can transfer the required charge to the load. Hence, the control inputs in  are all binary numbers, and only one member of aiy(t) and abat(t) is one. In this study, we omit this constraint. As a result, aiy(t) and abat(t) are nonnegative real numbers satisfying ∑iaiy(t) + abat(t) = 1.
- In the model in , it is assumed that at most one supercapacitor can be charged by the battery. This assumption is omitted in this paper.
3. Approximate Dynamic Programming Approach to Dynamic Power Management
3.2. ADP-Based Solution Procedure
- Choose the parameters of the problem: γ, λ, M, Rth, , , and .
- Estimate the 1st and 2nd moments of the external load demands, and , from the training data.
- Initialize the decision-making time t = 0, and choose x(0)= x0.
- Compute the stage cost matrix in Equation (30) and the constant matrix in Equation (64).
- Define the LMI variables:
- Define the basic LMI variables: Pi, pi, and qi in Equation (27).
- Define the derived LMI variables: Gi in Equation (39) and Si−1 in Equation (47).
- Define the S-procedure multipliers: in Equation (63).
- Find the approximate state value functions, , by solving the following convex optimization problem:
- Obtain the ADP controllers on the basis of
4. Simulation Results and Trajectories
4.1. An Illustrative Example
4.2. Discussions and Performance Comparison
Conflict of Interest
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Park, J.; Chung, G.-B.; Lim, J.; Yang, D. Dynamic Power Management for Portable Hybrid Power-Supply Systems Utilizing Approximate Dynamic Programming. Energies 2015, 8, 5053-5073. https://doi.org/10.3390/en8065053
Park J, Chung G-B, Lim J, Yang D. Dynamic Power Management for Portable Hybrid Power-Supply Systems Utilizing Approximate Dynamic Programming. Energies. 2015; 8(6):5053-5073. https://doi.org/10.3390/en8065053Chicago/Turabian Style
Park, Jooyoung, Gyo-Bum Chung, Jungdong Lim, and Dongsu Yang. 2015. "Dynamic Power Management for Portable Hybrid Power-Supply Systems Utilizing Approximate Dynamic Programming" Energies 8, no. 6: 5053-5073. https://doi.org/10.3390/en8065053