3.3.1. Current Prediction Model of Converter

In Boost mode, V<sup>2</sup> and the anti-parallel freewheeling diode D<sup>1</sup> are in working state. During the turn-on stage of switch V<sup>2</sup> (Sc<sup>2</sup> = 1), the energy storage unit charges the inductor *L* through V2, as shown in Figure 5a. Equation (4) can be obtained from its equivalent circuit, which is further discretized to obtain the predicted current value at the *k* + 1th moment, shown in Equation (5).

$$\text{Ld}I\_{\text{sto}}/\text{dt} = \text{U}\_{\text{sto}} \tag{4}$$

$$i\_{\rm sto}(k+1) = T\_{\rm s} \mu\_{\rm sto}(k)/L + i\_{\rm sto}(k), \tag{5}$$

where *u*sto(*k*) denotes the voltage detected at both ends of the energy storage unit (the battery or the supercapacitor) at the *k*th moment; *i*sto(*k*) represents the current of the energy storage unit, which flowing through inductance *L* at the *k*th moment and *T*<sup>s</sup> is the sampling period.

During the switching off stage of V<sup>2</sup> (SC2 = 0), the electromagnetic energy stored in inductance *L* is released to the DC side through the anti-parallel freewheeling diode D1. The following formula can be obtained from the circuit shown in Figure 5b.

$$\mathbf{L}\mathbf{d}\mathbf{l}\_{\rm sto}/\mathbf{d}t = \mathbf{U}\_{\rm sto} - \mathbf{U}\_{\rm dc\\_sto}.\tag{6}$$

Equation (6) is discretized and the predicted current is as follows.

$$i\_{\rm sto}(k+1) = T\_{\rm s}[\mu\_{\rm sto}(k) - \mu\_{\rm dc\\_sto}(k)]/L + i\_{\rm sto}(k),\tag{7}$$

where *u*dc\_sto(*k*) denotes the DC side voltage of the converter at the *k*th moment.

Similarly, when the bidirectional DC/DC converter operates in Buck mode, its prediction model of current is established as follows.

$$\begin{cases} \dot{\mathbf{u}}\_{\rm{sto}}(k+1) = T\_{\rm{s}}[-\mathbf{u}\_{\rm{sto}}(k) + \mathbf{u}\_{\rm{dc\\_sto}}(k)]/L + \dot{\mathbf{s}}\_{\rm{sto}}(k), & (\mathbf{S}\_{\rm{C1}} = 1) \\\ i\_{\rm{sto}}(k+1) = -T\_{\rm{s}}\mu\_{\rm{sto}}(k)/L + i\_{\rm{sto}}(k), & (\mathbf{S}\_{\rm{C1}} = 0) \end{cases} \tag{8}$$

where SC1 = 1 represents the conducting state of switch V1.
