## 3 Energy Management Strategies for Hybrid Tractors
### Second Layer Power Decoupling Based on Logic Rules  
After the Haar wavelet transform, the filtered signal removes the high-frequency part of the original signal, but the sub-high-frequency power signal still exists in \(P_{a}(n)\). In order to keep the PEMFC working in the high-efficiency zone as much as possible, the second layer of filtering decoupling is applied to the \(P_{a}(n)\) based on the logic rules.  
An energy distribution model based on a deterministic rule-based logic threshold control is used to decouple \(P_{a}(n)\). The tractor operation characteristics are combined to classify \(P_{a}(n)\) into different supply modes: hydrogen fuel cell powered mode (M1), multi-energy synergy model (M2), and maximum output mode (M3).  
Among them, in M1 mode, the hydrogen fuel cell alone undertakes low-frequency power; in M2 mode, the LiFePO4 battery can compensate for power outside the high-efficiency zone  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Filters** & **Parameters** & **Value** \\ \hline H0(Z) & b1 & \(-\)0.7071 \\  & b2 & 0.7071 \\ H1(Z) & b3 & 0.7071 \\  & b4 & 0.7071 \\ G0(Z) & b5 & 0.7071 \\  & b6 & \(-\)0.7071 \\ G1(Z) & b7 & 0.7071 \\  & b8 & 0.7071 \\ \hline \hline \end{tabular}
\end{table}
Table 1: State parameters of the two-channel quadrature filter bank.  
Figure 6: Block diagram of the power allocation.  
of the PEMFC system; in M3 mode, the hydrogen fuel cell outputs peak power within the logic rule, and the LiFePO4 battery compensates for the excess power.  
Considering that the hydrogen fuel cell has response hysteresis, the power fluctuation ratio is defined as \(\lambda_{tur}\), and the logic threshold rule limits the output power of the hydrogen fuel cell.  
\[\lambda_{tur}=\frac{P_{a}-P_{tur}}{P_{tur}} \tag{18}\]  
Set the threshold control parameters as follows: current hydrogen fuel cell power is \(P_{Q}\); low-frequency power is \(P_{a}(n)\); optimal hydrogen fuel cell power upper limit threshold is \(P_{Qlim}\); power fluctuation ratio of the hydrogen fuel cell is \(\lambda_{Q}\); power fluctuation ratio of the hydrogen fuel cell is \(\lambda_{\lim}\); power fluctuation ratio of the LiFePO4 battery is \(\lambda_{D}\); power fluctuation ratio threshold of the LiFePO4 battery is \(\lambda_{Dlim}\).  
Judgment conditions are set: \"\(P_{Qlim}>P_{a}\)\" is N1, \"\(P_{Qlim}\leq P_{a}\)\" is N2, \"\(\lambda_{Q}\leq\lambda_{Qlim}\)\" is N3, \"\(\lambda_{Q}>\lambda_{Qlim}\)\" is N4, \"\(\lambda_{D}\leq\lambda_{Qlim}\)\" is N5, \"\(\lambda_{D}>\lambda_{Dlim}\)\" is N6. Then the electric tractor's energy management logic rules are as follows:  
\[R=\left\{\begin{array}{l}T(N1\wedge N3\wedge N5)\to M1\\ T(N1\wedge N4\wedge N5)\to M2\\ T(N2\lor N6)\to M3\end{array}\right\} \tag{19}\]  
where \(R\) is the judgment rule.  
The logic threshold rule is shown in Figure 7. It can be seen that using the logic rule, the sub-high-frequency power in the low-frequency power is allocated to the LiFePO4 battery, while the steady-state power is allocated to the PEMFC. When a power surge occurs, if the demand power and its fluctuation ratio are within the allowed threshold, the hydrogen fuel cell will carry out all the power output; when the demand power or its fluctuation ratio exceeds the allowed threshold, the hydrogen fuel cell will only carry out the power output within the threshold of the rule fluctuation ratio. The part beyond the threshold will be provided by the LiFePO4 battery, thus realizing the second layer of decoupling of the low-frequency power.