*5.1. Life Extension Test by Using An Ultracapacitor*

An ultracapacitor is a link between source and load. When used in parallel with the battery, it smooths out the load on the battery whilst improving the source impedance seen by the load. This may be viewed as the battery supplying the energy and the ultracapacitor supplying the short term power. Furthermore, to use an ultracapacitor matters in a battery's life extension, due to the constrained voltage drop. Here, the duty ratio controls the loading between battery and ultracapacitor. Figure 5a,b shows voltage drop of 52 V/10 Ah battery pack, versus three duty ratios. For the first case, with a duty ratio of 20%, it presents the duty ratio of the battery's loading as 80%, and on the contrary, the UC's loading is 20%. In cases of duty ratios of 20%, 60%, and 80%, the terminal voltages were 47.4 V, 47.7 V, and 47.9 V, respectively. It shows the increased effect of constrained voltage drops of battery when increasing the duty ratio of ultracapacitor. Similar cases of 50 V battery pack were measured and are shown in Figure 6a,b. In Figure 6a,b, the blue line is the battery's discharge, and the red line is the battery in parallel connection with UC, by setting to 75% duty ratio. The UC effectively reduces the voltage drop and decreases the DOD of the battery.

**Figure 5.** (**a**) Voltage drop vs. duty ratio in constant-current discharge: (**b**) voltage drop vs. duty ratio in pulse discharge.

**Figure 6.** (**a**) Discharge current of battery and system (battery/ultracapacitor (UC)); (**b**) voltage drop of battery and system.

### *5.2. Estimation of OCV and IRs*

Two experiments in this section were carried out for confirming the achievability for developing an adaptive control scheme on monitoring of a reused battery's parameters, e.g., IRs and OCV simultaneously. Here, lithium-ion batteries were selected and integrated in nominal voltages of 52 V and 50.4 V modules to simulate reused batteries. Working voltage *vb* and current *ib* of a reused battery were inputs required. According to the electrical circuit model (ECM), the estimated battery voltage was formulated through estimating model parameters, <sup>θ</sup>ˆ*i*=1∼4. The target estimating parameters were *voc*(OCV) and internal resistances (*Rs* and *Rt*). *voc*, *Rs*, and *Rt* can be extracted from online estimation algorithms.

### 5.2.1. Experiment 1

The objective of this experiment was to verify the accuracy of the proposed method of estimating IRs and OCV. One module of 12.6 V in a 50.4 V battery pack was used and composed by a random discharge current. Each discharge cycle was lower than 5 s so as to simulate a random load. Figure 7a shows voltage drop, battery current, and estimating error separately in a, b, and c. The estimating error tends to zero after 150 s.

(**b**)

**Figure 7.** *Cont.*

**Figure 7.** (**a**) Terminal voltage, discharge current, and estimating error; (**b**) estimating model parameters, θˆ*i*, i = 1~4; (**c**) estimated Rs, Rt, and voc in Experiment 1.

The trajectories of estimating parameters are illustrated in Figure 7b, and the parameters, θˆ 1,θˆ 2, θˆ 3, and θˆ <sup>4</sup> approach values of 0.1, 19.99, 100, and 1127, respectively. *R*s*, R*t, and OCV are listed in Figure 7c. The trajectory of ohmic resistance relates the parameter, θˆ 1. The polarized resistance converges to 0.03 Ω, and the OCV converges gradually from 11.27 to 11.44 V.
