*2.2. Control Strategy*

The above model describes the basic mathematical problems of energy management issue, but in practice, we still need to consider the influence of aging on the model. Therefore, in the design of control strategy, battery aging characteristics are taken into account. For convenience of description, here we simply use the SOH (defined as the ratio of the current maximum capacity and the nominal capacity) to describe the different state of battery aging. The more specific parameters variations and the mathematical expression of the battery aging model will be further discussed in Section 3. Figure 2 shows the flow chart of the presented EMS. The blended control strategy [29] is used for power allocation, where the total power demand is split between the lithium battery pack and APU according to the control rules described below. To clearly illustrate the control algorithm, two thresholds are given at first, namely δ<sup>1</sup> and δ2, where the δ<sup>1</sup> denotes the high SOC level threshold and δ<sup>2</sup> denotes the low SOC threshold. If the battery SOC ≥ δ1, the battery will provide as much power to supply the load requirement; in this case, the optimization is not required. When battery SOC drops below the δ1, the control algorithm is given as below.

**Figure 2.** The schematic diagram of energy management strategy.

(1) When battery SOC is higher than the low threshold (SOC ≥ δ2),

$$P\_E = \max\left\{\psi\_{E\prime} \mid \frac{P\_{raq} - P\_{\text{Ratt\\_max}}(z, SOH)\eta\_{Ratt}}{\eta\_{APU}}\right\} \tag{8}$$

in which

$$\psi\_{E} = \begin{cases} P\_{\sigma \prime} & \text{if } \frac{P\_{mq}}{\eta\_{\#} \mu \prime l} \in (P\_{H\prime} P\_{E\\_\text{max}})\\ \quad P\_{opt\prime} & \text{if } \frac{P\_{pq}}{\eta\_{\#} \mu \prime l} \in (P\_L, P\_{H}]\\ \quad 0, & \text{if } \frac{P\_{pq}}{\eta\_{\#} \mu \prime l} \in [0, P\_L] \end{cases} \tag{9}$$

where *Popt* denotes the power of engine at its highest efficiency point, *PL* and *PH* are two thresholds to define a high efficiency range of the engine. *P*σ denotes the power demand of the engine that needs to be optimized.

The maximum output power of the battery pack is treated as a function of battery SOC and SOH, and is calculated by a discrete solving process [30]:

$$P\_{\text{Ratt\\_max},k}(z,SOH) = n\_{\text{Ratt}} \cdot \mathcal{U}\_{\text{tmin}} \left( \frac{\text{OCV}(z\_{k-1}, SOH\_{k-1}) - \mathcal{U}\_{p,k} - \mathcal{U}\_{\text{tmin}}}{\frac{\Delta t \eta\_{\text{Ratt}}}{Q\_{\text{Ratt}}(SOH\_{k-1})} \frac{\partial CCV(z)}{\partial z}|\_{z=z\_{k-1}} + R\_0(z\_{k-1}, SOH\_{k-1})} \right) \tag{10}$$

where *nBatt* is the number of the cells that contained in the lithium battery pack, *Ut*min is lower cut-off voltage, *z* denotes the battery SOC.

(2) When SOC is quite low (SOC < δ2), the battery pack stop discharging and the engine provides the power demand:

$$P\_E = \max\{0, \frac{P\_{req}}{\eta\_{APUI}}\} \tag{11}$$
