Distributed Nonlinear AIMD Algorithms for Electric Bus Charging Plants
Abstract
:1. Introduction
1.1. Motivation and Objective
1.2. Literature Overview
1.3. Contributions
1.4. Outline of the Paper
2. Methodology and Preliminaries
2.1. AIMD Algorithm
2.2. NAIMD Algorithm
3. Charging Process and Bus Characteristics
3.1. Power Plant and Depot Characteristics
- charging is executed after the service time when the buses are parked on the shunting area inside the depot;
- charging is also possible during the service time, by means of fast-charging spots at terminal stations.
3.2. Bus Characteristics
3.3. The Charging Rate Allocation Problem
4. The Adopted NAIMD Algorithm
4.1. Recast of the Battery Model in the NAIMD Framework
4.2. Minimization of the Sum of Charging Times
4.3. The Proposed NAIMD Solution
4.4. Convergence Considerations
5. Case Studies
5.1. Case Study 1: Charging Rate Allocation of an Existing Plant
5.2. Case Study 2: Sizing of a Bus Charging Plant
6. Concluding Remarks
Author Contributions
Funding
Conflicts of Interest
Abbreviations
AI | Additive Increase |
AIMD | Additive Increase Multiplicative Decrease |
CE | Capacity Event |
EMS | Energy Management System |
EV | Electric Vehicle |
LS | Least Square |
MD | Multiplicative Decrease |
NAIMD | Nonlinear Additive Increase Multiplicative Decrease |
SCADA | Supervisory Control And Data Acquisition |
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Bus i | (s) | (kW h) | (h min) | (h min) |
---|---|---|---|---|
1 | 1 | 34.14 | 3 h 18 | 3 h 18 |
2 | 538 | 5.6 | 3 h 35 | 3 h 44 |
3 | 538 | 109.11 | 1 h 59 | 2 h 8 |
4 | 784 | 85.93 | 2 h 47 | 3 h |
5 | 784 | 124.737 | 1 h 50 | 2 h 3 |
6 | 1252 | 90.47 | 2 h 10 | 2 h 31 |
7 | 1252 | 118.51 | 1 h 54 | 2 h 14 |
8 | 1311 | 102.58 | 2 h 3 | 2 h 25 |
9 | 1311 | 100.27 | 2 h 4 | 2 h 26 |
10 | 1637 | 148.54 | 1 h 35 | 2 h 3 |
11 | 1637 | 145.03 | 1 h 38 | 1 h 5 |
12 | 1637 | 24.04 | 3 h 24 | 3 h 52 |
13 | 1637 | 50.82 | 3 h 28 | 3 h 36 |
14 | 2218 | 66.62 | 2 h 59 | 3 h 36 |
15 | 2218 | 45.24 | 3 h 12 | 3 h 49 |
16 | 2218 | 121.80 | 1 h 52 | 2 h 29 |
17 | 2809 | 76.50 | 2 h 53 | 3 h 40 |
18 | 2809 | 82.67 | 2 h 49 | 3 h 18 |
19 | 2809 | 68.85 | 2 h 57 | 3 h 44 |
20 | 2809 | 50.66 | 3 h 8 | 3 h 55 |
21 | 2809 | 87.33 | 2 h 14 | 3 h 1 |
22 | 3023 | 141.22 | 1 h 40 | 2 h 30 |
23 | 3023 | 32.51 | 3 h 19 | 4 h 10 |
24 | 3049 | 103.74 | 2 h 3 | 2 h 53 |
25 | 3117 | 108.50 | 1 h 59 | 2 h 55 |
26 | 3117 | 137.10 | 1 h 43 | 2 h 38 |
27 | 3117 | 89.24 | 2 h 11 | 3 h 7 |
28 | 3117 | 89.70 | 2 h 11 | 3 h 6 |
29 | 3215 | 92.32 | 2 h 9 | 2 h 3 |
30 | 3441 | 44.60 | 3 h 9 | 4 h 6 |
(MW) | (h min) | (h min) |
---|---|---|
1 | 5 h 11′ | 9 h 44′ |
1.5 | 3 h 55′ | 7 h 50′ |
2 | 3 h 26′ | 7 h 1′ |
Bus i | 09:00 10:00 | 10:00 11:00 | 11:00 12:00 | 12:00 13:00 | 13:00 14:00 | 14:00 15:00 | 15:00 16:00 | 16:00 17:00 | 17:00 18:00 | 18:00 19:00 | 19:00 20:00 | 20:00 21:00 | 21:00 22:00 | 22:00 23:00 | 23:00 24:00 | 24:00 01:00 | 01:00 02:00 | 02:00 03:00 | 03:00 04:00 | 04:00 05:00 | 05:00 06:00 | 06:00 07:00 | 07:00 08:00 | 08:00 09:00 |
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J (h) | # CEs | |
---|---|---|
1 | 346.77 | 491 |
1.5 | 226.52 | 74 |
2 | 195.12 | 12 |
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Ravasio, M.; Incremona, G.P.; Colaneri, P.; Dolcini, A.; Moia, P. Distributed Nonlinear AIMD Algorithms for Electric Bus Charging Plants. Energies 2021, 14, 4389. https://doi.org/10.3390/en14154389
Ravasio M, Incremona GP, Colaneri P, Dolcini A, Moia P. Distributed Nonlinear AIMD Algorithms for Electric Bus Charging Plants. Energies. 2021; 14(15):4389. https://doi.org/10.3390/en14154389
Chicago/Turabian StyleRavasio, Matteo, Gian Paolo Incremona, Patrizio Colaneri, Andrea Dolcini, and Piero Moia. 2021. "Distributed Nonlinear AIMD Algorithms for Electric Bus Charging Plants" Energies 14, no. 15: 4389. https://doi.org/10.3390/en14154389