## 3 Energy Consumption Model and Theoretical Analysis  
A hydraulic press is a closed energy conversion system composed of electric energy, mechanical energy, hydraulic energy, and forming energy, and the total energy consumption of a single hydraulic press is in the form of electrical energy.  
Figure 4: Diagram of the proposed energy-saving buffer system.  
The required electrical energy of a hydraulic press is determined by the flow rate q and the working pressure p of the actuator, which changes with the operation stage. Taking into account the energy conversion efficiency of the hydraulic system, the electrical energy demanded (\(E_{electric-1}\)) by the hydraulic machine to complete forming actions can be expressed as Equation (1):  
\[E_{electric-1}=\sum_{i}\int_{T_{0}}^{T_{0}+T_{1}}p\cdot q\frac{1}{\eta_{Drive}}dt \tag{1}\]  
where stage \(i\) includes the PS stage and the FF stage; \(\eta_{Drive}\) is the energy efficiency of motor-pump units; \(T_{0}\) is the start time of stage \(i\); and \(T_{1}\) is the duration of stage \(i\).  
In terms of a hydraulic press with an energy-saving buffering system, Equation (1) can be divided into two parts,  
\[\begin{array}{ll}E_{electric-1}=&E_{1}+E_{2}\\ &=\sum_{i}\biggl{(}\int_{T_{0}}^{T_{0}+T_{1}}p_{TMP}\cdot q_{TMP}\frac{1}{ \eta_{Drive}}dt\\ &\qquad+\int_{T_{0}}^{T_{0}+T_{1}}p_{PFS}\cdot q_{PFS}dt\biggr{)}\end{array} \tag{2}\]  
where \(E_{1}\) and \(E_{2}\) are the energy provided by the traditional motor pumps and the prefill system, respectively; \(p_{TMP}\) and \(q_{TMP}\) are the pressure and flow rate provided by the traditional motor pumps, respectively; and \(p_{PFS}\) and \(q_{PFS}\) are the pressure and flow rate provided by the prefill system, respectively.  
Apart from the electrical energy demanded by the hydraulic main circuit during the FF and PS stages, other electrical energy (\(E_{electric-2}\)) demanded by the overflow circuit and the unloading circuit during the PM, PR, and WT stages can be expressed as Equation (3):  
\[E_{electric-2}=\sum_{e}\biggl{(}\int_{Tm}P_{1}dt+\int_{Tn}P_{2}dt+\int_{Ti}P_{ 3}dt\biggr{)} \tag{3}\]  
where \(P_{1}\), \(P_{2}\), and \(P_{3}\) are the motor power of the UL stage, the FR stage, and the WT stage, respectively; and \(Tm\), \(Tn\), and \(Ti\) are the duration of the UL, FR, and WT stages.  
Therefore, total energy consumption in a working cycle (\(E_{electric-Total}\)) can be obtained:  
\[E_{electric-Total}=E_{1}+E_{electric-2}. \tag{4}\]  
Since the hydraulic actuator does not output mechanical energy until the forming process completes, the forming energy (\(E_{Forming}\)) of one working cycle can be expressed as:  
\[E_{Forming}=\sum_{i}\int_{i}F_{NP}\cdot\textbf{{h}}dt \tag{5}\]  
where \(h\) is the height of the piston rod; and \(F_{NP}\) is the forming pressure of the hydraulic press.  
Therefore, the energy efficiency (\(\eta_{E-F}\), electrical-forming energy) of the proposed hydraulic press can be expressed as Equation (6):  
\[\eta_{E-F}=\frac{E_{Forming}}{E_{electric-Total}}. \tag{6}\]  
As shown in the above analysis, the integration of the prefill system and the buffer system can significantly reduce the power burden of traditional motor pumps during the high-load stage, and a reduction of installed power can be realized. In addition, both overflow losses during the PM stage and throttling losses during the idle state of the press could be greatly reduced because of the reduction of installed power, thereby improving the energy efficiency of the hydraulic press. Detailed energy-efficiency improvement is discussed in the following section.