Algorithms for Battery Utilization in Electric Vehicles

Figures & data

FIGURE 1 The penalty function.

Table

Algorithm 1. Current Allocation for a Single Request
Input: Current demand, d, battery capacities, .
1: Let be the number of batteries with a capacity of at least 1, i.e., .
2: if d ≤ 1 then {small request}
3:  if then
4:   Allocate the demand from x1, i.e., x1 = d.
5:  else
6:   CALL: GreedyAllocation.
7:  end if
8: else if d ≥ m then {large request}
9:  if then
10:   Determine initial allocation of xj = 1 from batteries .
11:   Allocate the remaining demand in a balancing way among batteries.
12:  else {}
13:   Determine initial allocation of xj = 1 from batteries .
14:   Allocate the remaining demand, i.e., , by GreedyAllocation.
15:  end if
16: else if then {midsized request: low-fraction request}
17:  if and then
18:   Determine initial allocation of xj = 1 from batteries .
19:   Allocate the remaining demand, i.e., , in a balancing way frombatteries .
20:  else
21:   if and then
22:    Determine allocation of for all batteries .
23:    Allocate the remaining demand, i.e., , by GreedyAllocation.
24:   else {}
25:    Determine initial allocation of xj = 1 from batteries .
26:    Allocate the remaining demand, i.e., , by GreedyAllocation.
27:   end if
28:  end if
29: else {midsized request: high-fraction request}
30:  if then
31:   Determine initial allocation of xj = 0.5 from batteries .
32:   Allocate the remaining demand, i.e., , in a balancing way frombatteries limiting the allocation from any single battery by 1,i.e., xj ≤ 1 for all j.
33:  else
34:   Determine initial allocation of xj = 1 from batteries .
35:   Allocate the remaining demand, i.e., , by GreedyAllocation.
36:  end if
37: end if
38: Update for all batteries .

Table

Algorithm 2. GreedyAllocation
Input: Current demand, d, battery capacities, , discharge currents,
1: i = m
2: while d > 0 do
3:  Set
4:  Update allocation,
5:  Update remaining demand,
6:  i = i–1
7: end while

FIGURE 2 Cases when the batteries’ status is not AboveTheLine.

FIGURE 3 Possible behavior of an online algorithm and the adversary.