MPC Framework for the Energy Management of Hybrid Ships with an Energy Storage System
Abstract
:1. Introduction
1.1. Regulatory and Technical Context for Battery Installations
- The shape of the efficiency curve of the prime mover is the dominant decisive factor for the applicability of an ESS installation
- When an ESS replaces engine power instead of adding power to an existing engine rating, the efficiency gains are smaller especially at nominal loads
- In electric propulsion, most conversion losses introduced by an ESS are already in place
- A DC grid allows for use of non-fixed-speed generator sets and consequently affects the powertrain efficiency in favour of using generator sets and not ESSs
- Efficiency gains in electric propulsion due to ESSs are found to be 4.7–7.8% at 50% load and 18–30% at 15% load.
1.2. Energy Management Stragegies and Problem Definition
1.3. Aim, Contributions and Assumptions
- Deals with battery-induced integral state constraints robustly.
- Realises potential fuel savings due to mission-scale information.
- Performs close to the exhaustive DP solution results.
- Can be readily set to function in charge-sustaining (CS) or charge-depleting (CD) battery mode.
- Enables real-time adaptation to shipboard updates on the mission-scale disturbance estimation while sailing, rather than using offline tuning of parameters such as the equivalency factor in ECMS, predefined power demand sequences [38] or rule-based tuning.
- Requires minimal parameter tuning on specific operating profiles enabling deployment on early design stages, with the prerequisite that a model description for the powertrain is available.
2. Materials and Methods
2.1. Model Description
- The electrical and mechanical nodes of the plant correspond to energy balance equations.
- For a given disturbance vector, which is typically comprised by the propulsive load, hotel load and shaft speed, the operating setpoints of the components are not uniquely defined due to the degrees of freedom (DoFs) in the system. For example, the propulsive demand can be met by infinite combinations of main engine and induction motor power output levels. The number of indefinite variables in the model description corresponds to the DoF in the system and each DoF correspond to an additional system control input.
- Each component introduces operating constraints which should be explicitly expressed.
- Finally, since the SoC of the battery must be within its operating constraints, it should be introduced to the system as a state variable.
2.2. Energy Management Strategy Framework
3. Results
3.1. Model Description Tuning and Verification
3.2. Verification of the Reference Trajectory Generator Module
3.3. Verification of the Model Predictive Control Module
- The state is the battery SoCk and it is sampled from the Simulink® model of the propulsive plant at each time step tk and used as the initial SoC for the OCP.
- The disturbances to the system are the shaft speed, propulsive power demand, and hotel power demand. The predicted values for each disturbance and for the scope of each horizon are provided to the OCP at each time step tk.
- The SoCMPC at the end of the horizon tk + NcΔt is constrained by the SoCref of the global solution at the same time-step. This is the ESC of Equation (32).
- The DP solver is utilised to provide the solution to the OCP above for the control horizon. The control inputs to the system are the normalized battery current In and electric machine torque Mn. The resulting control input vector for the next time step uk + 1 is fed to the system and the control input vectors for the rest of the time-steps, uk + 2…Nc, are discarded.
- At the next time-step the MPC module samples the next SoC and iterates the procedure.
3.4. Validation of the Model Predictive Control Framework
- The first online DP controller has perfect information about the disturbances, including the change at the IBP. This means that it is the optimal controller and calculates the control inputs for the telegraph trajectory spliced at the barrier point.
- The second online DP controller solves for the initial prediction until the IBP, where it recalculates the control inputs for the actual trajectory.
- The MPC framework’s RTG module is updated with the actual trajectory at the update point, which is before the IBP.
4. Discussion
- The MPC framework shows close-to-optimal performance and satisfies all operating constraints, including the integral constraints on the SoC, for all tested loading sequences and modes. A time interval of 600 s for both the prediction and the control horizon has been found to be sufficient for achieving such performance.
- In CD mode the consumption reduction due to utilisation of mission-scale predictions can be substantial. Compared to the fully-informed, optimal controller, the MPC framework selects higher power setpoints only after it receives the information for the updated profile, both in the standard and the parametric study (Figure 9a and Figure 10b). This means that the primary factor for reducing the fuel consumed is the use of all the energy in the battery. This in turn offsets the consumption of the main engines and the generator to lower values. A reduction of up to 3.5% was achieved for this specific case study in CD mode and under specific loading sequences. In CS mode, savings due to unused charge avoidance are not possible.
- When the induction motors are active, the reduction in fuel consumption due to mission scale information is possible (0.4% reduction observed). The control inputs from the MPC framework yield fuel-efficient operating points in the envelope of the main engine. This is achieved by storing energy, via the induction motors, to the battery plant and using it at a later time, in such a way that the fuel consumed is minimised.
- For several loading sequences, the two benchmark solutions coincide partially or completely. In such cases, few solutions that satisfy all of the OCP’s constraints exist, leading to a solution space where fuel consumption reduction due to use of mission scale information is insignificant. In the simulations for the MPC framework, the DP solvers in the RTG and MPC modules of the framework have been shown to be effective in finding these feasible solutions, adding to the controller’s robustness.
- The computational load allows for an embedded controller. The controller framework implemented in Simulink®, simulated together with the dynamic model, require less time to compute than the mission on a laptop computer.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
Parameter | Value | Units |
---|---|---|
PPTO/I,loss,nom | 1.9050 × 105 | W |
Tnom | 2.2037 × 105 | Nm |
Nnom | 2.1667 | s−1 |
mf,DE,nom | 0.4950 | kg/s |
PDE,nom | 9 × 107 | W |
NDE,nom | 16.667 | s−1 |
mf,DG,nom | 0.1481 | kg/s |
Pf,gen,nom | 2.6923 × 106 | W |
kp | 2 | |
nser | 34 | |
npar | 102 | |
Pcell,max | 1.8417 × 103 | W |
Qcell,0 | 48.06 | As |
Inom,los | 206.670 | A |
Ibat,AC,nom | 10287 | A |
pf | 0.8 | |
Vline | 440 | V |
iGB,B | 7.692 | |
iGB,drive | 1 | |
Mn,min | 0.3 | |
PDE,n,min | 0.45 | |
SoCmin | 0.2 | |
PDG,n,min | 0.4 |
Parameter | Value |
---|---|
CD | Charge Depleting |
CS | Charge Sustaining |
DAE | Differential and Algebraic Equations |
DoF | Degrees of Freedom |
DP | Dynamic Programming |
ECMS | Equivalent Consumption Minimisation Strategy |
EMS | Energy Management Strategy |
ESC | End-State Constraint |
ESS | Energy Storage System |
IBP | Information Barrier Point |
IC | Internal Combustion |
MPC | Model Prodictive Control |
OCP | Optimal Control Problem |
PTO/I | Power take-off/in |
RTG | Reference Trajectory Generation |
SFOC | Specific Fuel Oil Consumption |
SoC | State of Charge |
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Profile/Telegraph Position | Fuel Consumption [kg] | Difference [%] |
---|---|---|
Base | 1974.3 | |
−10% | 1908.1 | −3.35 |
+10% | 2085.5 | +5.63 |
50% PDE,nom | 2055.1 | +4.09 |
50% Tnom | 2056.7 | +4.17 |
Profile 1 | Profile 2 | |||
---|---|---|---|---|
Fuel Consumption [kg] | Difference [%] | Fuel Consumption [kg] | Difference [%] | |
Optimal | 1787 (1961) | −4.85 (−3.44) | 1758 (1949) | 0.00 (−0.20) |
Barrier | 1878 (2031) | 1758 (1953) | ||
MPC | 1811 | −3.57 | 1798 | +2.28 |
Fuel Consumption [kg] | |||
---|---|---|---|
600 s | 1200 s | 1800 s | |
Optimal | 1787 | 1787 | 1787 |
Barrier | 1878 | 1878 | 1878 |
MPC | 1811 (−3.56%) | 1813.4 (−3.44%) | 1842 (−1.92%) |
Fuel Consumption [kg] | |||
---|---|---|---|
1 MW | 5 MW | 7.27 MW | |
Optimal | 1787 | 2442 | 2825 |
Barrier | 1878 | 2447 | 2839 |
MPC | 1811 (−3.56%) | 2448 (+0.04%) | 2826 (−0.44%) |
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Antonopoulos, S.; Visser, K.; Kalikatzarakis, M.; Reppa, V. MPC Framework for the Energy Management of Hybrid Ships with an Energy Storage System. J. Mar. Sci. Eng. 2021, 9, 993. https://doi.org/10.3390/jmse9090993
Antonopoulos S, Visser K, Kalikatzarakis M, Reppa V. MPC Framework for the Energy Management of Hybrid Ships with an Energy Storage System. Journal of Marine Science and Engineering. 2021; 9(9):993. https://doi.org/10.3390/jmse9090993
Chicago/Turabian StyleAntonopoulos, Spyros, Klaas Visser, Miltiadis Kalikatzarakis, and Vasso Reppa. 2021. "MPC Framework for the Energy Management of Hybrid Ships with an Energy Storage System" Journal of Marine Science and Engineering 9, no. 9: 993. https://doi.org/10.3390/jmse9090993