**1. Introduction**

Energy consumption in the transportation and the industrial sector represented 72% of the total energy consumption during 2018 in the United States. Most of this energy (around 87%) comes from petroleum-based sources and natural gas [1]. In the industrial sector, around 24% of the energy is spent by the agriculture, construction, and mining sectors. Many applications within these sectors use hydraulic equipment and hydraulic machinery, so improving the energy efficiency of the hydraulic systems that are already in use could have a large impact on the reduction of energy consumption and emissions. If the energy efficiency of the hydraulic machinery used in industrial applications is improved by 5%, based on the data provided by the U.S. Energy Department [1], it is possible to estimate an overall annual reduction of 1% in energy consumption in the US.

Over the last 20 years, there has been interest in developing and improving systems for energy regeneration in hydraulic machinery [2–5]. Some of the options for energy storage in energy regeneration devices include flywheels, compressed air, electrical energy storage systems (EESS), and hydraulic

energy storage systems (HESS). In the electrical energy regeneration system, an electric accumulator or capacitor is used to store energy [6]. This kind of system is used in electric hybrid machinery. The return line of a boom mechanism in an excavator is connected to a hydraulic motor that is used to move an electric generator that produces electrical energy that is stored in an electric accumulator (ultracapacitor or battery) [2,3,7]. The main benefit of this system is an improvement in energy efficiency, but the complexity that is added to the baseline hydraulic system is evident. Ultracapacitors are mostly used in electric applications that require a high power density such as wind turbines in remote areas [8], energy regeneration and engine size reduction in rubber wheeled gantry cranes [9], and even biomedical applications [10].

The hydraulic energy regeneration system is similar to its electric counterpart. Instead of having an electric accumulator (ultracapacitor or battery), the hydraulic energy regeneration system uses a hydraulic accumulator that works as the energy storage device [6]. One of the main benefits when using a hydraulic regenerative system is the relative ease of installation, since the baseline application already uses a hydraulic system. Moreover, no complex power controls are needed, which is a significant advantage. On the other hand, the energy storage density in hydraulic accumulators can be a drawback when compared to a traditional electric system. Hydraulic regenerative systems have been studied for applications in relief valves [11], where the flow in the return line of the valve is used to charge a hydraulic accumulator. Alternatives like digital hydraulics have been studied to improve energy efficiency in hydraulic systems [12,13]. In these studies, a network of valves is used to change the flow rate in the actuator and to reconfigure the system in order to use the flow from assistive loads to move actuators with resistive loads.
