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This paper proposes formulating conceptual-stage vessel design optimization problems as geometric programs, which can be transformed into convex optimization problems. Convex optimization offers significant advantages in efficiency, reliability and automation potential over the general nonlinear optimization approach typically used in naval architecture. Focusing on battery-electric vessels, geometric program compatible models are derived for lithium-ion cells, power converters, propulsion motors and propellers. Preliminary hull form development, stability calculation and structural design are also presented in the context of geometric programming. The modeling approach is applied to study optimal battery sizing for a coastal bulk carrier sailing in varying operational conditions. Using open-source software tools, the battery sizing problem is solved in less than a second on a standard desktop computer. Local sensitivity information encoded by optimal dual variables reveals that increasing the cell discharge upper bound by 1% decreases the optimal total number of cells by more than 1%. On the other hand, the sensitivities of cell volume and maximum discharging current parameters are zero, indicating that the constraints involving these parameters do not govern the solution.

We present a reinforcement learning (RL) model that is based on Q-learning for the autonomous control of ship auxiliary power networks. The development and application of the proposed model is demonstrated using a case-study ship as the platform. The auxiliary power network of the ship is represented as a Markov Decision Process (MDP). Q-learning is then used to teach an agent to operate in this MDP by choosing actions in each operating state which would minimize fuel consumption while also respecting the boundary conditions of the network. The presented work is based on an extensive data set received from one of the cruise-line operators on the Baltic Sea. This data set was preprocessed to extract information for the state representation of the auxiliary network, which was used for training and validating the model. As a result, it is shown that the developed method produces an autonomous control policy for the auxiliary power network that outperforms the current human operated manual control of the case-study ship. An average of 0.9 % fuel oil savings are attained over the analyzed round-trips with control that displayed similar robustness against blackouts as the current operation of the ship. This amounts to 32 tons of fuel oil saved annually. In addition, it is shown that the developed model can be reconfigured for different levels of robustness, depending on the preferred trade-off between maintained reserve power and fuel savings.

This paper evaluates the effect of a large-capacity electrical energy storage, e.g., Li-ion battery, on optimal sailing routes, speeds, fuel choice, and emission abatement technology selection. Despite rapid cost reduction and performance improvement, current Li-ion chemistries are infeasible for providing the total energy demand for ocean-crossing ships because the energy density is up to two orders of magnitude less than in liquid hydrocarbon fuels. However, limited distance zero-emission port arrival, mooring, and port departure are attainable. In this context, we formulate two groups of numerical problems. First, the well-known Emission Control Area (ECA) routing problem is extended with battery-powered zero-emission legs. ECAs have incentivized ship operators to choose longer distance routes to avoid using expensive low sulfur fuel required for compliance, resulting in increased greenhouse gas (GHG) emissions. The second problem evaluates the trade-off between battery capacity and speed on battery-powered zero-emission port arrival and departure legs. We develop a mixed-integer quadratically constrained program to investigate the least cost system configuration and operation. We find that the optimal speed is up to 50% slower on battery-powered legs compared to the baseline without zero-emission constraint. The slower speed on the zero-emission legs is compensated by higher speed throughout the rest of the voyage, which may increase the total amount of GHG emissions.

We present a novel convex optimisation model for ship speed profile optimisation under varying environmental conditions, with a fixed schedule for the journey. To demonstrate the efficacy of the proposed method, a combined speed profile optimisation model was developed that employed an existing dynamic programming approach, along the novel convex optimisation model. The proposed model was tested with 5 different ships for 20 journeys from Houston, Texas to London Gateway, with differing environmental conditions, which were retrieved from actual weather forecasts. As a result, it was shown that the combined model with both dynamic programming and convex optimisation was approximately 22% more effective in developing a fuel saving speed profile compared to dynamic programming alone. Overall, average fuel savings for the studied voyages with speed profile optimisation was approximately 1.1% compared to operation with a fixed speed and 3.5% for voyages where significant variance in environmental conditions was present. Speed profile optimisation was found to be especially beneficial in cases where detrimental environmental conditions could be avoided with minor speed adjustments. Relaxation of the fixed schedule constraint likely leads to larger savings but makes comparison virtually impossible as a lower speed leads to lower propulsion energy needed.

We present a novel methodology for the control of power unit commitment in complex ship energy systems. The usage of this method is demonstrated with a case study, where measured data was used from a cruise ship operating in the Caribbean and the Mediterranean. The ship’s energy system is conceptualized to feature a fuel cell and a battery along standard diesel generating sets for the purpose of reducing local emissions near coasts. The developed method is formulated as a model predictive control (MPC) problem, where a novel 2-stage predictive model is used to predict power demand, and a mixed-integer linear programming (MILP) model is used to solve unit commitment according to the prediction. The performance of the methodology is compared to fully optimal control, which was simulated by optimizing unit commitment for entire measured power demand profiles of trips. As a result, it can be stated that the developed methodology achieves close to optimal unit commitment control for the conceptualized energy system. Furthermore, the predictive model is formulated so that it returns probability estimates of future power demand rather than point estimates. This opens up the possibility for using stochastic or robust optimization methods for unit commitment optimization in future studies.

This study investigates the potential of improving the energy efficiency and reducing the lifecycle costs of electric city buses with multispeed gearboxes. A two-speed dual clutch gearbox and a continuously variable transmission were studied and compared to a reference fixed gear ratio powertrain. A novel two-level optimization model was introduced. The top level involves an exhaustive search algorithm and quasi-static vehicle dynamic model for optimizing the two-speed gearbox gear ratios, utilizing efficiency maps for the electric motor and the inverter. The second level is an integer programming model, which finds an optimal gear shifting policy subject to constraints on hysteresis and gear shifting induced losses. The model was applied with a standard driving cycle and additionally with three measured cycles acquired from a prototype battery electric city bus operating on a daily schedule on a suburban route in Espoo, Finland. The results showed that a two-speed gearbox reduced energy consumption by 2–3.2%, depending on the driving cycle characteristics. On the other hand, the continuously variable transmission was found to increase consumption by 1.9–4.0% due to large losses of the belt mechanism. It was concluded that the two-speed gearbox is a cost-effective investment for electric city buses characterized by operation profiles with frequent acceleration and braking events.

Uncertainty in operation factors, such as the weather and driving behavior, makes it difficult to accurately predict the energy consumption of electric buses. As the consumption varies, the dimensioning of the battery capacity and charging systems is challenging and requires a dedicated decision-making process. To investigate the impact of uncertainty, six electric buses were measured in three routes with an Internet of Things (IoT) system from February 2016 to December 2017 in southern Finland in real operation conditions. The measurement results were thoroughly analyzed and the operation factors that caused variation in the energy consumption and internal resistance of the battery were studied in detail. The average energy consumption was 0.78 kWh/km and the consumption varied by more than 1 kWh/km between trips. Furthermore, consumption was 15% lower on a suburban route than on city routes. The energy consumption was mostly influenced by the ambient temperature, driving behavior, and route characteristics. The internal resistance varied mainly as a result of changes in the battery temperature and charging current. The energy consumption was predicted with above 75% accuracy with a linear model. The operation factors were correlated and a novel second-order normalization method was introduced to improve the interpretation of the results. The presented models and analyses can be integrated to powertrain and charging system design, as well as schedule planning.