## 2 Materials and Methods  
The machine used was a horizontal decanter centrifuge BABY-1 from \"Pieralisi\" available in the laboratory, with an operating throughput of 500 kg/h, coupled to an asynchronous three-phase induction motor (IM) by \"ABB\" with 5.5 kW of nominal mechanical power. The connection between the electric motor and horizontal centrifuge is established by pulleys and two toothed drive belts with a measured gearbox ratio of 1.7365. A timetable, arising from a real olive oil mill, was used to simulate the activity period of the device constituted by motor + decanter (MD). When considering the overall working time per day, from the timetable it arises that the MD is run unloaded for 6% of its daily operating time, while the MD is run loaded for the rest of the daily operating period (94%). We considered a 40-day working period, with increasing working hours per day at the start (first nine days) from 7 to 20 and decreasing working hours per day at the end (last seven days) from 20 to 7, with a plateau of 20 h per day in the middle (consisting of the remaining 24 days). The results of the simulation have been used in conjunction with the previously described timetable over a 40-day campaign period. Some assumptions have been made:  
1. The dilution ratio (i.e., the ratio between the mass of added lukewarm water and the mass of olive oil paste) is considered to be 0.2 (the normal dilution ratio for high-quality extra virgin olive oil extraction);
2. The horizontal centrifuge full productive capacity is considered to be exactly equal to 500 kg/h. From the operational timetable previously described, it arises that the overall processed product was 226,685 kg on 627 overall working hours, the time that the horizontal centrifuge was run unloaded was 37.62 h, and the time that the horizontal centrifuge was run at full load was 589.38 h.  
The final results considered are the following: the overall energy consumption per processed product unit mass (OSEC) expressed as kJ/kg; the overall specific energy wasted (i.e., the difference between the active power and the mechanical power at the motor shaft) per processed product unit mass (OSEW) arising from the wasted power considered as the overall (MD) centrifuge and electric motor wasted electrical power, expressed as kJ/kg; and, finally, the overall process efficiency (OPE) obtained by the following relation (OSEC-OSEW)/OSEC. The relations are the following. OSEC = (ActivePower \(\times\) TimeDecanterLoaded + ActivePower \(\times\) TimeDecanterUnloaded)/OverallProcessedProduct  
OSEW = (WastedPower \(\times\) TimeDecanterLoaded + ActivePower \(\times\) TimeDecanterUnloaded)/OverallProcessedProduct  
\[\text{OPE = (OSEC - OSEW)/OSEC}\]  
The configuration of the centrifuge coupled to a 5.5 kW electric motor, connected directly to the power line (DOL), was assumed as a reference for the comparison of subsequent simulations. Table 1 presents the fundamental reference parameters obtained when connecting the MD machine with the M4 motor-connected DOL. Matlab R2024a Simulink software (using Simscape Electrical, formerly SimPower-Systems) from MathWorks was used to simulate the physical system; the simulation was continued until a steady-state condition was reached. The use of asynchronous motors (identified as M2, M3, M4, M5, M6, and M7) was hypothesized with, respectively, a 3.0 kW, 4.0 kW, 5.5 kW, 7.5 kW, 11 kW, and 15 kW electric power, to investigate the optimal connection between the horizontal centrifuge and the electric motor. The motors were hypothesized to be driven by an electronic driver, i.e., an electronic VFD. The VFD measured efficiency was 0.95. The simulation concerned various cases, from an oversized IM to an overloaded IM, also testing various connections of the six motors and the horizontal centrifuge--varying the gearbox ratio for this reason--and between the electric line and the IMs using the VFD.