*5.4. Electric Drive Performance*

In this section, an evaluation of the proposed control scheme, using a Minimum Emissions Point Tracking algorithm, based on a gradient vector optimization technique, is presented. Simulation results include two different torque steps at 1 and at 2 , both representing different shaft power operational conditions *Ps* @ 90% rated power as base condition before 1 , de-rating to 60% of rated power in 1 , and finally going to 80% rated power at 2 .

Figure 15 shows the performance of the electric drive (the performance of the PMSM) in terms of its controlled currents. At low operational load below 75% of rated power, the MEPT algorithm sets the electric machine's torque reference in the generator region, therefore the torque producing current *iq* < 0, whereas the flux producing current *id* = 0. On the other hand, when entering into a high load condition above the minimum SFC point, the MEPT, forces the PMSM to operate in the motor region, therefore the torque producing current *iq* > 0, while the flux producing current *id* = 0.

**Figure 15.** Electric drive performance *id iq* during torque demand step.

In Figure 16 the tracking performance of the optimization algorithm is shown, in the presence of a step change of the diesel engine torque. As shown, the torque electric reference *T*∗*e* presents a fast and accurate response and keeps on tracking the minimum emissions operation point.

**Figure 16.** Optimization algorithm step dynamic response.

The grid side currents dynamic performance is shown in Figure 17, showing a sinusoidal behavior and fast dynamic response, during the transition from PTI to PTO mode at 1 and from PTO to PTI operation at 2 . Moreover, the fast tracking dynamics of the optimization algorithm, ensures minimization on the current wave-form distortion. On the other hand, due the fact that the grid side control scheme is decoupled from the electric drive control scheme, and ensures zero reactive power flow, the amplitude of the grid side currents are dependent on the electric drive's torque reference.

**Figure 17.** Grid side currents performance.

### **6. Conclusions and Future Work**

Results of the fuel consumed by the engine when simulating the PTO and PTI conditions are not ye<sup>t</sup> significant in helping to reduce EEOI values at both operating regions, which means less operational CO2 emissions.

The control scheme, when simulating the engine performance at PTI operating region, makes the engine work closer to the MEOP, which leads to low SFC, and therefore low operational emissions.

The control scheme shows the high reliability and accuracy to follow the optimization algorithm with good dynamics, at both operating conditions as PTI and PTO. It also ensures bidirectional power flow, with low distortion of in the grid side currents.

The optimization function presents an accurate performance to obtain a local search for the minimum emissions point, starting at a random state. Future results may include the use of an adaptive perturbation function to ensure full convergence when reaching the minimum emissions point.

Slow steaming was mentioned because of the application of the scheme ye<sup>t</sup> needs to be worked out separately from a design stage to provide more accurate conclusions to this work.

The ship and engine data considered for the simulations is open source and provides grea<sup>t</sup> value to continue to be used in this research.

Future work will consider the application of the proposed hybrid propulsion control scheme in a small-scale vessel for experimental validation of the SFC performance, as well as adding a more accurate operational profile of the vessel to work in depth the auxiliary engines and WHRS operational emissions generation influence.

**Author Contributions:** Conceptualization, J.R.P. and C.A.R.; methodology, J.R.P. and C.A.R.; simulation and programming, C.A.R.; validation, J.R.P. and C.A.R.; formal analysis, J.R.P.; investigation, J.R.P. and C.A.R.; data curation, J.R.P.; writing—original draft preparation, J.R.P. and C.A.R.; writing—review and editing, J.R.P. and C.A.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors wish to thank the financial support from the Chilean Found for Human Resource Development (CONYCIT) through its Ph.D. scholarships (CONICYT/21130448).

**Conflicts of Interest:** The authors declare no conflicts of interest.
