Energy Storage Management of Maritime Grids

Abstract

Generally, energy storage is the capture of energy produced at one time for use at a later time. Since these energy shifting or shaving abilities, energy storage can act as the role of generation or demand in different time-periods. This ability has shown great potentials to change the conventional operation pattern of power systems, i.e., the real-time power balance between the generation-side and demand-side. As a special type of power system, maritime grids are also applicable platforms for energy storage integration, such as in propulsion systems, or for energy recovery, and renewable energy integration. With the development of various energy storage technologies, energy storage will soon become indispensable equipment in maritime grids, and the energy storage management will become essential correspondingly. This Chapter focuses on the energy management of energy storage in maritime grids. At first, the energy storage technologies and their great effects on the power system operation are introduced. Secondly, the characteristics of different energy storage technologies are described. After that, the applications of energy storage in maritime grids are illustrated, (1) for the navigation uncertainties and demand response, and (2) for the renewable energy integration, and (3) for the energy recovery. At last, two practical problems are studied to show the energy management schemes of energy storage to address navigation uncertainties and to extend battery lifetime, respectively.

6.1 Introduction to Energy Storage Technologies

Energy is an essential commodity and a key element for global development, and generally comes from various sources and can be mainly classified as two types, (1) the primary forms of energy and (2) the secondary forms of energy. The primary forms of energy are those energy sources that only involve extraction or capture, and the energy directly comes from nature. Typical examples are crude oil, coal, various renewable energy, natural uranium, and falling or flowing water. On the other hand, the secondary forms of energy include all the energy forms after the transformation from the primary forms of energy. The relationship between the primary forms and the secondary forms are shown in Fig. 6.1.

Fig. 6.1

Primary and secondary energy [1]

Secondary energy forms are generally more convenient to use and usually viewed as “energy carriers”, including various types of petroleum, diesel, and electricity. The transformation technologies include oil refinery, thermal power plants, nuclear power plants, solar power plants, and so on. Among all the secondary forms of energy, electricity is the main “energy carrier” for daily lives, and power system is the corresponding man-made network to generate, transmit, and distribute electricity. Conventionally, the generation-side and demand-side of power system should be equal all the time since the electricity cannot be stored. Nowadays, with large scale of energy storage, power system will have more flexibility since energy storage can change its roles between the generation-side and the demand-side.

As a special type of power system, maritime grids also complete similar roles of “generate-transmit-distribute” as conventional power systems. For example, a seaport microgrid purchases electricity from the upper grid, and the electricity transmits to the seaport via the main substation and then distributes to different equipment within the seaport. Similarly in ships, the main and auxiliary engines generate electricity and the electricity is transmitted and distributed by the shipboard microgrid to various load demands. In this sense, energy storage also plays an essential role to facilitate the optimal operation of maritime grids.

For ships, in [2, 3], energy storage is coordinated with the propulsion system of an AES to achieve better economic and environmental targets. Then in [4], energy storage is used to supply the energy consumption of the shipboard gas capture system. In short-term timescale, [5,6,7] use energy storage to mitigate propulsion fluctuations. For seaports, [8,9,10] classify the energy storage as an individual agent and has its energy plans to participate in the seaport operation. Molavi et al. [11] uses energy storage to facilitate renewable energy integration. Later on, [12, 13] use energy storage to recover the energy when the lifting-down of port cranes. The above literature has clearly shown that energy storage has already been an important device in maritime grids, and proper management is essential for maritime grids.

This Chapter focuses on this topic and is organized as follows. Section 6.2 gives the characteristics of different energy storage technologies, and Sect. 6.3 gives several application cases of energy storage in maritime grids. At last, Sect. 6.4 analyzes two typical problems to demonstrate the effects of energy storage management.

6.2 Characteristics of Different Energy Storage Technologies

6.2.1 Classifications of Current Energy Storage Technologies

In this section, Fig. 1.13 is re-drawn here to show the classifications of energy storage and denoted as Fig. 6.2. This Chapter focuses on conventional energy storage technologies and fuel cell will be discussed in detail in Chap. 8. The nomenclature of various energy storage technologies is shown in Table 6.1.

Fig. 6.2

Classification of energy storage

Table 6.1 Nomenclature of different energy storage technologies

In the following Table 6.2, the characteristics of different energy storage are given. Since the different characteristics, we can find that different energy storage has quite different application scenarios. In the following context, some energy storage technologies which are used in maritime grids are described in detail to show their applications.

Table 6.2 Characteristics of different energy storage [14, 15]

6.2.2 Battery

Among current energy storage technologies, the battery is one of the most common technologies available on the market. The battery stores energy in the electrochemical form and the battery cells are connected in series or in parallel or both to make up the desired voltage and capacity. A typical battery packs’ structure is shown as Fig. 6.3, and each battery cell consists of two electrodes and an electrolyte, which are sealed in a container and then integrated into the external grid or load.

Fig. 6.3

Illustration of battery energy storage packs

In the last decade, the technologies of battery have become much more mature, such as the lead-acid battery, nickel-cadmium battery, lithium-ion battery. Especially for lead-acid batteries, which have been researched for over 140 years and is the most mature battery technology now. Currently, tremendous efforts have been carried out to turn technologies like nickel-cadmium and lithium-ion batteries into cost-effective options for higher power applications, and their lifetimes are also important research topics.

6.2.3 Flywheel

FES stores energy as the form of kinetic energy in a rotating mass or rotor. The stored energy is proportional to the rotor mass, location of the mass, and the rotor’s rotational speed. When FES charges, it absorbs the energy from outside and accelerates the rotating speed of mass. On the other side, when the flywheel discharges, the rotating mass drives a generator to produce electrical power, and the rotating speed slows down. An illustration of flywheel energy storage is shown in Fig. 6.4.

Fig. 6.4

Illustration of flywheel energy storage

Compared with other types of energy storage, FES can quickly respond to the power demand, and therefore be widely used in improving the power quality, load demand peak shaving, power factor correction, and load leveling. Other applications of flywheels include UPS [16], frequency response [17], smoothing wind power [18], and heavy haul locomotives [19].

The advantages of FES can be illustrated as it provides intermediate characteristics in terms of power and energy density compared with batteries and super-capacitor, i.e., the FES has much higher power density than batteries and much higher energy density than supercapacitors. Besides, FES also caters with many shortcomings of prior energy storage technologies, i.e., less sensitivity to temperature, chemical hazardless, higher life cycle, reduced space, and weight, which is suitable for many applications. But the FES also has its shortcoming, i.e., the complex maintenance process for rotating mass.

6.2.4 Ultracapacitor

Capacitors store energy in the electric field and have a quite low equivalent series-resistance that enable them to supply the power efficiently. Generally, the capacitors are used in higher power demand scenarios, including the compensation of reactive power, mitigation of load fluctuations, and power quality issues. Capacitors usually can be classified as super-capacitors, electrolytic capacitors, and electrostatic capacitors. Figure 6.5 illustrates the typical structure of a super-capacitor. The main advantages of super-capacitors are higher power density, faster charging and discharging, longer life cycles compared with other energy storage technologies. The disadvantages are the low voltage of each cell, and much higher investment cost per Watt-hour, i.e., more than 10 times compared with a lithium battery. Other drawbacks of super-capacitor include relatively low energy density, linear discharge voltage, and high self-discharge.

Fig. 6.5

Illustration of super-capacitor energy storage

6.3 Applications of Energy Storage in Maritime Grids

6.3.1 Roles of Energy Storage in Maritime Grids

Generally, energy storage in maritime grids has three main applications, (1) as the main energy source, and (2) for long-term load leveling, shifting or shaving; and (3) for short-term power balancing.

Using energy storage as the main energy source is a recent trend for some short-trip ferries or cargo ships. Such as the first all-electric ferry “ampere” in North Europe [20], and China’s first all-electric cargo ship “puffer” in 2019 [21]. Until now, there are more than 50 ships using energy storage as the main energy source in Europe. The biggest capacity is 4.16 MWh (Li-ion), the smallest capacity is 0.02 MWh (Lead-acid). The all-electric ships are about to develop in China and there will be more ships launched in the future. The advantage of using energy storage as the main energy source is nearly zero-emission, but the disadvantage is also obvious, i.e., the capacity of current energy storage technologies is limited to individually sustain a large ship for a long-distance voyage. Similar in seaports and other ocean platforms, the capacity of current energy storage is just enough to serve as auxiliary equipment. In this sense, the main application scenarios of energy storage are still in the long-term load leveling and short-term power balancing.

For the long-term load leveling, the energy storage should have enough energy density to sustain a long-time discharging. Battery is generally the main equipment to undertake this task. Nowadays, many maritime grids have installed energy storage as essential auxiliary equipment for better system characteristics. Two recent examples in China are provided as following Fig. 6.6.

Fig. 6.6

Two cases for energy storage integration in maritime grids

The first example is the emergency supporting ship launched on April, 28th, 2020 in Shenzhen [22]. This ship has a length of 78 m and 12.8 m breadth. The deadweight is 1450 tons. The propulsion system has three diesel generators (3 × 2080 kW) and two Li-ion batteries (2 × 750 kW). The second example is in Lianyungang Port which plans a battery installment (1 MW ultracapacitor + 4 MW Li-ion battery) for cold-ironing services [23]. The above two examples are both using energy storage for long-term load-leveling (hours or even longer).

For short-term power balancing, energy storage should have enough power density. This task is usually undertaken by the ultracapacitor [5] or flywheel [6], since they have enough power density and can quickly respond to the power fluctuations. Jiang et al. [24] gives a schematic of electric propulsion system with ultracapacitor, which is shown as Fig. 6.7.

Fig. 6.7

Schematic of an electric propulsion system with ultracapacitor

In Fig. 6.7, the EMS sends control signals to the electric power generation and DC/DC converter to determine their power outputs. Then the electric power generation and ultracapacitor are both used to supply the propeller.

The applications of energy storage in maritime grids are briefly described above. To further clarify the applications, three scenarios are selected and analyzed in detail, i.e., navigation uncertainties and demand response, renewable energy integration, and energy recovery.

6.3.2 Navigation Uncertainties and Demand Response

Chapters 3 and 4 have discussed the influences of navigation uncertainties on the maritime grids. To mitigate these uncertainties, maritime grids should reserve a certain “sea margin” or “spinning margin” which can quickly respond [25]. For a maritime grid, the influences of navigation uncertainties can be described as the changes in load demands. Figure 6.8 gives an example of how energy storage mitigates the navigation uncertainties.

Fig. 6.8

Power sharing by energy storage

From the following Fig. 6.8a, the total power demand has two peaks. The main energy source need to suffer fast ramping-ups/ramping-downs, or frequent shut-downs/start-ups to follow the power demand. The influences of navigation uncertainties are similar to Fig. 6.8a, i.e., leading to many peak loads. When integrating energy storage, the main energy source and energy storage can share the total power demand, shown as Fig. 6.8b. The charging/discharging of energy storage can smooth the power demand and make the main energy source working in a steady-state, and the economic and environmental behaviors may be both improved. In this sense, energy storage integration has been viewed as an important approach to facilitate the operation of maritime grids.

It should be noted that energy storage can level/smooth other types of power demand in maritime grids as well, such as service load [3], or weapon system [26], and even in some short-term timescale applications [5,6,7]. In those applications, the effects are similar to Fig. 6.8a, b, i.e., the main energy source keeps a nearly constant power output and the energy storage shares the fluctuated load demand by continuous discharging/charging. This advantage also gives a new requirement for energy storage management, i.e., the energy storage should coordinate with the main energy source to achieve economic and environmental tasks.

6.3.3 Renewable Energy Integration

To resolve the bottleneck of energy efficiency problems in maritime grids, renewable energy has been gradually integrated into and may soon become an essential part of maritime grids. However, as we have mentioned in Chaps. 1 and 4, the renewable energy is less controllable compared with conventional energy, and the power outputs are generally fluctuating all the time and cannot be accurately forecasted. There are many routes to mitigate the influences of renewable energy and energy storage integration is an important way [24, 27, 28]. Reference [24] gives a schematic diagram of battery energy storage to mitigate the wind power fluctuations, which is shown in Fig. 6.9.

Fig. 6.9

Power sharing by energy storage [24]

From Fig. 6.9, the battery units are installed with the wind turbine in parallel. Two layers of control strategy are used to determine the battery power for compensating the wind power fluctuation. In the first layer, the wind power is measured and the fluctuation mitigation control layer determines the compensating power. Then the power allocation control layer split the power into each battery unit, including the charging/discharging states and power values. With this compensation, the power output fluctuation of a wind turbine can be greatly reduced.

6.3.4 Energy Recovery for Equipment

With the electrification of various equipment in maritime grids, energy storage can be used as an energy buffer to recover the wasted energy for later usage. Binti Ahamad et al. [13] has studied the energy recovery by energy storage for an electrified port crane. Figure 6.10 shows 8 working steps for an electrified port crane. The corresponding power demand is shown in Fig. 6.11.

Fig. 6.10

Typical working steps for a port crane

Fig. 6.11

Reprinted from [29], open access

Power demand curves for a port crane.

A typical working process of a port crane includes (1) hoist, or beginning to lift up; (2) lifting up speedily; (3) lifting up speedily and the trolley moving forward; (4) lifting up with the full speed and the trolley moving forward; (5) lifting up with slowing speed and the trolley moving with full speed; (6) the trolley moving with slowing speed; (7) lifting down speedily and the trolley moving with slowing speed; (8) settling down. Step (2) and (3) usually have the biggest power demand whereas steps (6), (7) and (8) have smaller power demands. Furthermore, when the cargo is lifting down, the gravitational potential of cargo is wasted, which accounts for about 20% of the total energy consumption [13].

Reference [13] uses a flywheel to store the energy when the cargo is lifting down. The entire process consists of three modes, including mode 1: grid provides power and flywheel discharge; mode 2: grid provides power and flywheel charges; and mode 3: crane charges the flywheel, and three modes are shown in Fig. 6.12. The fourth sub-figure shows the operating cycle of the flywheel.

Fig. 6.12

Power demand curves for a port crane [13]

In Fig. 6.12, mode 1 is used when the power demand is high, and mode 2 is used when the power demand is low, and mode 3 is used when the cargo is lifting down. From the overall scope, the flywheel has a periodical operation pattern between “discharging-charging-standby” to recover energy. In a seaport microgrid, there will be increasing electrified equipment and many of them are used for the lifting up/lifting down cargos. Therefore energy storage will be widely used in the future.

6.4 Typical Problems

6.4.1 Energy Storage Management in AES for Navigation Uncertainties

• (1) Voyage scheduling and navigation uncertainties

In general, the navigation uncertainty forecasting includes pre-voyage forecasting and intra-voyage forecasting [30]. Responding to the pre-voyage forecasting navigation uncertainties is widely known as the weather routing problems, or pre-voyage planning [30,31,32]. But the conventional ships are rather difficult to respond to the intra-voyage navigation uncertainties, since in conventional ships, the prime motors are connected with propellers via shafts and gearboxes, and the speed regulation ability of conventional ships are therefore limited. With the development of electric propellers, the prime motors can be “physically separated” from the propellers by the shipboard electric network. With the aid from integrated ESSs, the onboard generation of AESs can quickly and economically respond to the intra-voyage navigation uncertainties. In the future AESs, both the pre-voyage and intra-voyage navigation uncertainties should be addressed by proper energy management.

• (2) Two-stage scheduling framework

As shown in Fig. 6.13, the first stage is to respond to the pre-voyage navigation uncertainties and gives the on/off states of onboard DGs, and the second stage is to respond to the intra-voyage navigation uncertainties and gives the loading factors of onboard DGs and other decision variables. The merits are as follow:

Fig. 6.13

Relation between the first and second stage of proposed model, reprinted from [33], with permission from IEEE

• a. The two-stage operation model can respond to the pre-voyage navigation uncertainties and intra-voyage navigation uncertainties, coordinately, to gain a compromise between the robustness and flexibility, i.e., the first stage for the worst operating case (robustness) and the second stage to adapt to the current operating case (flexibility).

• b. With the proposed two-stage operation, the management of onboard DGs can be more convenient, since the on/off states of onboard DGs are determined before a voyage. The arrangements of the repair or overhaul of the onboard DGs are much easier.

In the pre-voyage time-window, i.e., the first stage, the decision variables are optimized based on the pre-voyage forecasting navigation uncertainty set. The decision variables in the first stage include on/off states of onboard DGs and their loading factors, the shipboard ESS power, the propulsion load and the cruising speed. This stage is to find an optimal robust shipboard operating scheme for addressing the worst speed loss case caused by navigation uncertainties. In this stage, only the on/off states of DGs are “here-and-now” variables and remain as constants in the second stage. Other variables, including the loading factors of DGs, shipboard ESS power, propulsion load, and cruising speed are all “wait-and-see” variables, which will be re-dispatched in the second stage towards uncertainty realization. In the intra-voyage time-window, i.e., the second stage, the navigation uncertainties are treated as realized. All of the “wait-and-see” variables are re-dispatched to address the short-term navigation uncertainties.

The proposed two-stage robust model can be viewed as a “predictive-corrective” process. The first stage is the predictive process to respond to the worst-case and the second stage is the corrective process which takes recourse actions to compensate for the first stage, i.e., reducing the conservatism of the first stage.

• (3) Case study

To test the proposed two-stage robust optimization problems. Two methods are compared as follows, and the cruising speed and EEOI comparisons are shown in Fig. 6.14.

Fig. 6.14

Reprinted from [33], with permission from IEEE

Cruising speed and EEOI comparisons.

Method A (Non-robust model): shipboard generation scheduling with the expected wave and wind.

Method B (Robust model): the proposed robust shipboard generation scheduling (first stage and second stage models). In the second stage, an uncertainty sample is selected from the uncertainty set to represent the uncertainty realization.

Firstly, the on-time rates are obtained by generating 500 navigation uncertainty samples in the uncertainty set. The voyage distance of each sample in the terminal port is shown in Fig. 6.15.

Fig. 6.15

Reprinted from [33], with permission from IEEE

On-time rates of robust and non-robust models.

In the proposed two-stage robust model, the cruising speed will increase compared with the non-robust model since the robust model is to meet the worst case of the navigation uncertainties, meanwhile, the non-robust model only needs to cope with the expected uncertainties. In this sense, the non-robust model cannot guarantee the on-time rates of AES.

To analyze the effects of energy storage on the navigation uncertainties, the total battery power and SOC in the first and second stages are shown in Fig. 6.16.

Fig. 6.16

Reprinted from [33], with permission from IEEE

Multi-battery ESS scheme in first and second stages.

From Fig. 6.16, since the worst-case assumed in the first stage may not happen, the total battery power is reduced in the second stage. This phenomenon also shows that the proposed two-stage model can well adapt to the uncertainties with sufficient flexibility.

6.4.2 Energy Storage Management in AES for Extending Lifetime

• (1) Definitions of DoD and MSOC

In general, improper cycling conditions are the main reasons for battery degradation, i.e., charging/discharging cycles and the DoD in each cycle [34,35,36,37]. In recent years, the impacts of MSOC on the battery lifetime have been gradually realized, but still not been incorporated into the operation problem, yet. In fact, DoD and MSOC are two main factors we considered in the battery degradation. The DoDs and initial/terminal SOCs of battery in discharging/charging events are defined in Fig. 6.17a, b.

Fig. 6.17

Reprinted from [38], with permission from IEEE

Definitions of the DoD and initial/terminal SOCs.

In Fig. 6.17, when a charging/discharging event begins, the SOC of battery is denoted as the initial SOC, and when this event terminates, the SOC is denoted as the terminal SOC. The SOC variations between the initial and terminal SOCs are defined as the DoD, denoted as $d$. The middle point of the initial and terminal SOCs is defined as the MSOC, denoted as $SOC^{mean}$.

Since the ship generally has multiple batteries, for the b-th battery in the i-th charging/discharging event, the DoD is denoted as $d_{i}^{b}$, and the corresponding MSOC is denoted as $SOC_{b,i}^{mean}$, and the equivalent life cycle (ELC) is denoted as $ELC_{b,i} = \mathop \sum \limits_{i} d_{i}^{b}$.

In the following, we use a vector to denote the MSOC-DoD combination hereafter, i.e., ($SOC_{b,i}^{mean} ,d_{i}^{b}$). For example, (0.3, 0.6) means the experiment is conducted in $SOC_{b,i}^{mean} = 0.3$ and $d_{i}^{b} = 0.6$.

• (2) Impacts of DoD and MSOC on the battery lifetime

In the former section, two main factors for battery degradation have been defined, i.e., $d_{i}^{b}$ and $SOC_{b,i}^{mean}$. In the following, a battery degradation model is formulated based on the above two factors. The original dataset is based on experimental research of battery health [39]. It has 14 aging experiments for the batteries in the same brand. The discharging/charging current in each experiment is the same and there are five MSOC-DoD combinations, i.e., (0.3, 0.6), (0.5, 0.2), (0.5, 0.6), (0.5,1), (0.7, 0.6). Several experimental data are shown in Fig. 6.18a, b. If the MSOC-DoD combination is the same, it refers to the experiment that has been conducted twice, otherwise, the experiment is only conducted for once.

Fig. 6.18

Reprinted from [38], with permission from IEEE

Experimental data illustration.

In Fig. 6.18, the horizontal axis represents the ELC. The vertical axis represents the normalized battery capacity, and it will decay with the charging/discharging cycles. From above, the impacts of DoD and MSOC on the battery lifetime are clear, i.e., smaller DoD and lower MSOC lead to smaller battery degradation. The reasons are shown as follows, (1) in Fig. 6.18a, experiment 1–6 share the same MSOCs but the DoDs are different, i.e., from 0.2 to 1. As shown in the dataset, the battery with higher DoD will have faster degradation, and (2) in Fig. 6.18b, experiment 7–10 share the same DoD but the MSOC are different, from 0.3 to 0.7. As shown in the dataset, the battery with higher MSOC suffers from higher battery degradation.

To show an example for battery degradation calculation, we take the curve of experiment 6 as an example. The battery in experiment 6 has 879 cycles before life ending. Then the average degradation in each cycle in p.u. is $De_{i}^{b} = \frac{1 - 0.8}{879} = 2.2 \times 10^{ - 4}$. Similarly, the average degradations in each cycle for 14 experiments are calculated. For clarification, we denote the obtained battery degradation dataset as $\left( {SOC_{b,i}^{mean} ,d_{i}^{b} ,De_{i}^{b} } \right), b \in {\mathcal{B}}$, where $De_{i}^{b}$ is the average battery degradation.

• (3) A revised data-driven battery degradation model

According to Ref. [34], the model of battery lifetime versus DoD is shown as (6.1), where $k_{1}$, $k_{2}$ and $k_{3}$ are all fitting coefficients. To reflect the impacts of MSOC, the degradation model shown in Eq. (6.1) should be revised, and Table 6.3 shows different fitting models and their R-square parameters under the dataset [39]. The fitting tools used is the “sftool” in Matlab 2016b.

Table 6.3 Different Fitting Models and parameters

$$ De_{i}^{b} = k_{1} \cdot \left( {d_{i}^{b} } \right)^{{k_{2} }} \cdot e^{{k_{3} \cdot d_{i}^{b} }} $$

(6.1)

From the results of Table 6.3, model 1and 2 share the best R-square 0.91 with its maximum equal 1, and model 1 is selected as the final battery degradation model since fewer fitting variables and shown as the following Fig. 6.19.

Fig. 6.19

Reprinted from [38], with permission from IEEE

Fitting surface of Battery degradation vs. DoD and MSOC.

In Fig. 6.19, the black points are the original dataset points, and the fitting surface has shown clear dependence of DoD and MSOC on battery degradation, i.e., higher MSOC and larger DoD will cause higher battery degradation. With the above battery degradation model, the lifetime of battery can be shown as (6.2).

$$ L_{i}^{T} = \frac{1 - 0.8}{{De_{i}^{b} }} = \frac{0.2}{{De_{i}^{b} }} $$

(6.2)

where $1 - 0.8$ means the battery lifetime terminates when the normalized battery capacity becomes 0.8 of its full capacity; $L_{i}^{T}$ is the battery lifetime under charging/discharging event $i$. Obviously, if we want to extend the battery lifetime $L_{T}$, $De_{i}^{b}$ should be minimized.

• (4) Multi-battery scheduling

For indicating when and how many batteries should be utilized, a task matrix $B^{A}$ is defined and Eq. (6.3) gives an example with the entire operating period having 4 time-intervals, i.e., $t_{1} \sim t_{4}$, and the shipboard ESS include 4 batteries, i.e., no. 1–4.

$$ B^{A} = \left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} 1 & 1 \\ 1 & 1 \\ \end{array} } & {\begin{array}{*{20}c} 0 & 0 \\ 0 & 0 \\ \end{array} } \\ {\begin{array}{*{20}c} 0 & 1 \\ 0 & 1 \\ \end{array} } & {\begin{array}{*{20}c} 1 & 1 \\ 1 & 1 \\ \end{array} } \\ \end{array} } \right] $$

(6.3)

In (6.3), the row represents batteries and the column represents time-intervals. $B^{A} \left( {i,j} \right) = B_{i,j}^{A} = 1$ represents battery i will be switched-on to share power demand (charging or discharging) in the j-th time-interval, or $B^{A} \left( {i,j} \right) = B_{i,j}^{A} = 0$ represents the battery i will stand by. With the above definition, the process of multi-battery management can be shown in Fig. 6.20.

Fig. 6.20

Reprinted from [38], with permission from IEEE

Multi-battery management into two-stage operation.

With the above multi-battery ESS management, different batteries or battery groups can share different charging/discharging events, which has the potential to reduce the cycles of each battery. The overall lifetime of multi-battery ESS maybe therefore extended.

• (5) Case study

To show the benefits of the proposed model, three methods are compared with each other.

Method A: Conventional energy management without considering battery lifetime degradation [2].

Method B: Conventional energy management only considering DoD as the battery lifetime determinant [34].

Method C: Proposed energy management without multi-battery management.

It should be noted that methods A–C are used to calculate the battery power, and the battery degradations of three methods are calculated by the same model proposed (Model 1 in Table 6.3). The power and SOC curves of three methods are shown in Fig. 6.21, and the corresponding battery degradation in each voyage and overall lifetime are shown in Table 6.4.

Fig. 6.21

Reprinted from [38], with permission from IEEE

Battery power schedules and SOCs of three cases.

Table 6.4 Battery degradation and lifetime in three methods, reprinted from [38], with permission from IEEE

In this case study, the voyage is divided into two parts, i.e., $t = 0\sim 35$ and $t = 41\sim 64$ are in cruising states, and $t = 36\sim 40$ is in berthed-in state. From the results in Fig. 6.21, batteries in method A–C all tend to discharge when cruising states to share the power demand and to charge when berthed-in state. It is mainly because when berthed-in, the propulsion load is zero and to avoid frequent start-ups/shut-downs of onboard generators, the energy will be stored in the battery for later usage.

However, with different battery degradation model, method A–C have different DoDs and MSOCs. In method A, the battery degradation is not considered, the battery operating scheme tends to fully use the battery to reduce $FC^{DG} + FC^{ST}$, and the DoDs of t = 0–35, t = 36–40 and t = 41–64 are 0.8, 0.79, and 0.27, respectively. Meanwhile, in method B, the DoD is considered as the only decision variable of battery degradation. Then the battery operating scheme tends to limit the DoDs, in which the DoDs of t = 0–35, t = 36–40, t = 41–64 decrease to 0.6, 0.6, and 0.27. As a result, the battery lifetime of method B increases by 35.6% compared with method A from Table 6.4. This phenomenon clearly shows that DoD is an important factor for battery lifetime.

In the proposed model (method C), the DoD and MSOC are considered as two factors for battery lifetime. Then compared with method B, method C reduces the MSOC of $t = 0\sim 35$,$t = 36\sim 40,$ and $t = 41\sim 64$ from 0.8, 0.8, and 0.87 (method B) to 0.49, 0.5, and 0.66 (method C). Correspondingly, the battery lifetime of method C increases by 51.9% compared with method A, and 12% longer than method B.

The above phenomenon clearly shows that both the DoD and MSOC have vital impacts on the battery lifetime. The proposed test case has 4 batteries, and each battery has 4 MWh capacity and 2.5 MW power, which is denoted as 1–4. 4 batteries are in two groups. Battery 1, 2 are group 1, and battery 3, 4 are group 2. Method D is designed to show the advantages of multi-battery management. The battery power of methods C and D are shown in Fig. 6.22.

Fig. 6.22

Reprinted from [38], with permission from IEEE

Battery power schedules and SOCs of method C and D.

Method D: Proposed energy management with multi-battery management.

From Fig. 6.22, with the multi-battery management, the power demand in different time periods is shared by battery 1 + 2 and 3 + 4, respectively. For example, when $t = 0\sim 13$, the power demand is undertaken by battery 1 + 2, and when $t = 14\sim 36$, battery 3 + 4 undertake the power demand. With this strategy, the battery degradations are shown in Table 6.5.

Table 6.5 Battery degradation and lifetime in method C and D, reprinted from [38], with permission from IEEE

From the above results, the implementation of multi-battery management can further reduce the MSOC of battery 3 + 4, which leads the battery 3 + 4 only have $1.07 \times 10^{ - 3}$ MWh degradation compared with $1.84 \times 10^{ - 3}$ in method C. As a result, battery 1 + 2 must undertake more power demand than battery 3 + 4, so their degradations increase to $2.19 \times 10^{ - 3}$. In total, the battery degradation in method D is still lower than method C.

In the next voyage, battery 1 + 2 and battery 3 + 4 will change their roles. Battery 1 + 2 will lower their MSOC and battery 3 + 4 will undertake more power to protect the health of battery 1 + 2. With this strategy, the multi-battery management can further extend the total battery lifetime by 12.7%, and the lifetime increases from 869.5 cycles to 980.3 cycles.

As above, the proposed shipboard multi-battery management method can be viewed as a coordinated operation of all the onboard batteries. One battery group undertakes most of the power demand and make the other one working in an MSOC with lower degradation. Then in the next voyage, the battery groups change their roles for the iterative usages.