1. Introduction
Shipping is one of the most economical modes of transportation and plays an important role in the global economy. As the container transportation industry has developed over the past 20 years, the size of container ships and the number of containers that they accommodate have increased [
1,
2,
3,
4,
5]. Accordingly, the construction of bigger ships, which is a confirmed method of reducing container shipping costs, is gradually accelerating [
6,
7,
8]. By building bigger containers ships, advantages such as economies of scale for marine logistics and transportation, reduction of construction costs, and securing competitiveness in the fierce cargo market can be obtained [
9,
10,
11,
12]. Otherwise expressed, reduced fuel consumption per unit of distance, and the overall reduction in operating costs due to shortened operation times on regular routes can be anticipated thanks to the trend toward larger container ships. [
13,
14,
15]. However, as the sizes of ships increase, so does the propulsion equipment, and the electrical load of a large ship requires significant rapid fluctuations in supply, leading to voltage and frequency deviations. A common approach for mitigating this is to over-design and maintain spinning reserves. However, this method adds weight, increases costs, and requires additional space [
16,
17,
18,
19]. Accordingly, as the size of the engine room increases, the size of the cargo hold decreases. Because the ship is for the transport of cargo, it is essential to design the capacity of the appropriate equipment. The size of the generator that supplies power to the ship is calculated in consideration of the safety margin along with the setting of the maximum usable load [
20,
21,
22,
23,
24].
Yuan, Y. et al. [
25], based on the existing power system, analyzed an actual ship’s experimental data under the conditions of arrival, departure, and normal sailing, and redesigned the solar system of the hybrid power system. Ghenai, C. et al. [
26] analyzed the electrical load of Dubai Ferries to optimize the design of an energy system that included solar power, fuel cells, and diesel generators. Ibrahim, S.H.A. et al. [
27] designed and optimized a solar system integrated with an existing diesel grid system by comparing four different combinations of hybrid systems. Wu et al. [
28] proposed optimal energy management based on a tabu-search-based heuristic control method to reduce fuel cost and obtain a reliable energy system. Bukar, A. et al. [
29] applied the meta-heuristic optimization algorithm Grasshopper Optimization Algorithm (GOA) to determine the optimal size of PV/wind power/battery/diesel generators. Aazami, R. et al. [
30] determined the capacity of the energy storage systems through a compensation method that reduces power fluctuations and stabilizes the frequency of the system. Leem, J. et al. [
31] calculated the optimal generator capacity through the PCF (Polynomial Curve Fitting) value obtained by analyzing the total load data to increase energy efficiency. Jung, S. et al. [
32] formulated a merging problem of multi-objective optimization and game theory approach to obtain the optimal capacity of a hybrid system. Deng, S. et al. [
33] suggested a PLCB (part-load properties-based) model in which the efficiency of the power generation device changes according to load fluctuations and performed the optimization of the capacity configuration of the energy hub. In calculating the generator’s capacity, the existing calculation method obtains the generation capacity where the maximum load is 80~90% of the total generation capacity. However, present methods do not optimize the generator capacity because this capacity is overestimated for safety reasons.
This study proposes a generator capacity estimation method to obtain high efficiency for large, refrigerated container ships. The novelty of this study is to prevent unnecessary overdesign of the power system and to calculate the generator’s capacity based on the result of analyzing the actual log data and aim for the optimal operation of the diesel generator.
In addition, the number and combination of generators were changed to meet the load requirements that change according to the operating conditions to suggest a strategy. The document is structured as follows.
Section 2 provides an overview of the ship’s architecture, loads, and resources.
Section 3 derives the GCI (Generator Capacity Index) for estimating the optimal generator capacity after analyzing the characteristics of each operation mode.
Section 4 classifies cases according to GCI values and compares the fuel consumption, operating time, and efficiency of generators. Finally, this paper draws a conclusion.
2. Ship Architecture
The subject ship of the present study is a super-large container ship with a size of 13,154 TEU (twenty-foot equivalent unit). The ship can load 1200 FEU (forty-foot equivalent unit) refrigerated containers and consumes approximately 7440 kW of power when operated at the maximum load.
Figure 1 shows the power system of the target ship, and
Table 1 lists the specifications of the ship.
The power supply of the power system comprises four generators with an installed overall capacity of 15,200 kW. Among the loads on the ship, two bow thrusters that are heavy consumers of approximately 2500 kW of power are installed. The data of the target ship were collected every 10 min after operating for approximately 397 days. The ship’s data that were used are speed, operation mode, rpm of the propulsion engine, required power, and power supplied by the generators. The power consumption of the ship’s load varies according to the operation mode, and the operation mode is generally classified as “At sea”, “Port in/out”, and “In port”.
The ship’s operation mode follows the order of “In port”, “Port in/out”, “At sea”, and “Port in/out”. When “Port in/out” occurs after “In port”, the operation is expressed as “Departure”, and before “Port in/out”, “In port” is expressed as “Arrival”. “At sea mode” occurs after the ship loads cargo from a port and travels to a target port. It operates at a relatively constant speed and takes up most of the voyage time. The power consumption is constant, and the load fluctuation is low. “Port in/out” mode is a process for a ship to anchor in a port at sea, and the speed change is large as the propulsion engine is operated at maneuvering rpm. It consumes the lowest time of operation, and the magnitude and volatility of power consumption are high. In “In port” mode, the propulsion engine is not used. It consumes the lowest load, and the load variability is also low.
Figure 2 shows the operating time in each mode.
Figure 3 shows the change in the load and operation mode of the ship according to the time the data were acquired, “0, 1, and 2 modes of the ship” indicate “In port”, “At sea”, and “Port in/out” modes, respectively.
Figure 4 is a graph showing as quartiles the distribution of power consumption during the ship’s operation modes. The horizontal axis of the figure indicates the number of times the operation mode was active during the time the data were acquired.
“At sea” mode was checked 58 times, and power in the range of approximately 1000–3500 kW is required owing to the refrigeration containers. When low numbers of containers are shipped, power use is in the 1500–2000 kW range. “In port” mode was checked 72 times, and power required is in the 1000–1500 kW range, and the load deviation is also small. “Port in/out” mode was checked 129 times, and it requires a high load depending on operations that require heavy power consumption. When heavy consumers are operating, power use is in the 2000–2500 kW range. In general, 1500–3000 kW of power is required, regardless of the mode. Accordingly, it seems appropriate to select the capacity that can operate the generator most efficiently in the 1500–3000 kW range. In addition, when using a heavy consumer, the peak load increases; therefore, the stability of the power supply must be ensured.
Figure 5 shows the generator load factor of the collected data.
The load factor of the generator exhibits the highest efficiency at about 80%, and the lower the load factor, the lower the efficiency. However, in the collected data, the load factor of the running generator operated in the 30–60% range at a rate of approximately 52.2%, and the load factor of the generator operating under 30% at a rate of 33.9%. This indicates that the generator actually operates with low efficiency, taking into account excessively the redundancy of the generator capacity. A diesel generator consists of a prime mover that consumes fuel to generate rotational force and a generator that converts rotational force into electric power. Put simply, a generator consumes fuel to produce electricity. Essentially, machine efficiency means output power versus input power; therefore, the input of the generator is the amount of fuel and the output is the amount of power. Equation (1) shows the power (kWh) produced per unit of fuel (g) consumed according to the load factor of the generator.
where
(%) is the load factor of the generator, and
(g/kWh) represents the fuel consumption of the generator when the current load factor is
(%).
Figure 6 shows the specification fuel oil consumption curve (SFOC), which plots the consumption according to the load factor of the generator obtained using Equation (1). The SFOC curve shows that the fuel consumption is the lowest in the range of 80–85%.
Accordingly, the power generation efficiency can be obtained using Equation (2).
where
(g/kWh) is the minimum fuel consumption per output unit, and
(g/kWh) represents the fuel consumption per output unit when the load factor of the generator is 0 (%).
A power management system (PMS) governs the generator operation, and directs the start and stop actions, heavy consumer management, and load distribution. If the load factor of the generator currently in operation is higher than the set load factor of the PMS, the generator is additionally started. At this time, as the number of generators increases, the set load factor increases.
Table 2 shows the set load factor according to the number of operating units designated in this study. The load factor can vary depending on the required power and total capacity of the generator in operation.
3. Generator Capacity Index
The subject ship is equipped with the generator of the same capacity; however, to apply the proposed strategy, two sets of generators with different capacities were configured. The GCI value indicates the capacity ratio of the generator; that is, the optimal capacity ratio between two different generators is derived by changing the capacity of the large generator based on that of the small generator. The capacity ratio is based on a generator with a relatively low capacity, and the GCI for a low-capacity generator is expressed as . This value is always 1. In addition, the GCI of the generator with a relatively high capacity is denoted by .
For example, when the total capacity of the generators is set to 10,000 kW, the fuel consumption according to the
value can be obtained as shown in
Figure 7. At this time, the load of the ship requires power in the range of 1000–8000 kW.
From
Figure 8, it can be seen that the optimal point of SFOC varies according to
. The lower the SFOC, the higher the efficiency. Conversely, the higher the SFOC, the lower the efficiency.
Figure 7 shows the efficiency of the generator according to
when the load profile is as shown in
Figure 8.
It can be seen that the efficiency is as high as 97.7–98.2% when the value of
is in the range of 1.3–1.8. Moreover, when the value of
is 1.5, the operation combination of the generator is evenly utilized for the required load for it to respond efficiently.
Table 3 shows the efficiency of each
as quartiles.
To apply and compare the proposed GCI strategy, a case was set and simulation was performed. At this time, the generators were operated in an optimal combination according to the required load. The optimal combination is the combination that has the lowest fuel consumption for the current demand load among the combinations that can be obtained through the configuration of four generators. The optimal combination can be obtained through the Algorithm 1 below.
Algorithm 1. Find optimal combination of generator is |
Input: Capacity of Each Generator , , , |
PMS Heavy Load Parameter [], |
Demand Load L, |
Output: Optimal combination Comb [OC] |
|
SFOC [] = {} |
Comb [] = {} |
for i = 1 to len(Comb []) do |
LF = L/( × 100 |
If [len(comb [i])] > LF then { |
SFOC [i] = |
} |
else { |
SFOC [i] = inf |
} |
OC = Index (SFOC [], minimum(SFOC []) |
|
Return Comb [OC] |
Assuming that the median value of the load required in “At sea” mode, which consumes most of the time during the operation of the ship, is
(kW), the capacity of the small generator is as follows:
Based on this, the capacity of the generators according to the
values is shown in
Table 4. Case 1 is a comparison target that verifies the effectiveness of the proposed strategy with reference to the previously designed strategy. In Case 2, the capacity of the small generator derived from Equation (3) is fixed, and the capacity of the large generator increases according to the
value. Accordingly, the total power of the generator increases for each case. At this time, to supply adequate power to the load of the ship, checking the total capacity of the generator is necessary. The container ship considered in this study is equipped with 1200 FEU (forty-foot equivalent units) of reefer container. In general, each reefer container requires approximately 6.2 kW of power, and because a reefer container is classified as a preference trip, it is not a problem even if the power supply is cut off for a short time. However, if the power supply to the reefer container is cut off for a long time, the temperature of the cargo cannot be guaranteed. Therefore, assuming that the entire reefer container is used in “At sea” mode, which is operated for a relatively long time, the inboard power system should supply stable power. At this time, the required maximum load is 9874 kW, and because the normal continuous rating (NCR) of the generator must meet the maximum load at the 85% point, the total power supplied by the generator needs to be at least 11,616 kW; that is, when classifying the simulation cases, the minimum value of
is 1.3.
4. Simulation
The simulation yields the fuel consumption (tons), generator operation time (hours), and efficiency (%) for each case. The simulation satisfies the following conditions:
- (1)
The generator is always operated in a combination that can satisfy the optimum SFOC.
- (2)
Fuel consumption by idle running of the generator is not considered
- (3)
Idle running of the generator is not included in the operation time of the generator.
- (4)
The load factor of the generator does not exceed the set load factor.
- (5)
The load profile considered in the simulation uses actual ship operation data, and the time interval is 10 min.
Figure 9 illustrates the simulation procedure of this study. The simulation environment was configured in NI’s Labview, and the fuel consumption and efficiency of the generator were calculated based on the required load/demand, which was the input data in the simulation, and the total cost was derived.
4.1. Fuel Consumption
First, the fuel consumption by case is listed in
Table 5. According to the table, there is no significant difference between the fuel consumption in the “Port in/out” and “In port” modes because the operating time is short; however, consumption in “At sea” mode determines the difference in total fuel consumption.
For the required load in the “At sea” mode, every case has a combination of one small generator and one large generator. Accordingly, as the value increases, the total generator capacity increases, and the operating load factor decreases. On comparing the previously designed capacity and fuel consumption for all the operation modes, the smaller the , the lower the fuel consumption. In the “At sea” mode, compared to the existing capacity, fuel consumption reduced from a minimum of 12 tons to a maximum of 53 tons according to . This is because the fuel consumption increases as the value increases; that is, the capacity of the generator increases, and the load factor decreases according to the rated output, resulting in low-load operation. In the “Port in/out” mode, fuel was reduced from a minimum of 4 tons to a maximum of 7 tons. In the “In port” mode, fuel savings of approximately 20 tons from Cases 2 to 6 were confirmed.
4.2. Efficiency
Efficiency for each case was derived based on Equation (3).
Figure 10 shows the power generation efficiency for each case, and
Table 6 shows the quartile of the efficiency for each case.
On comparing the previously designed capacity and efficiency for all the operation modes, the smaller the among the cases, the higher the efficiency. In the “At sea” mode, the efficiency increased from a minimum of 3.1% to a maximum of 8.4% according to compared to the existing capacity. This is because the efficiency decreases as increases; that is, the higher the generator capacity, the lower the load factor according to the rated output, and consequently the fuel consumption increases. In the “Port in/out” mode, the efficiency increased from 16.8% to 17.3%. Here, the reason for only 0.5% difference depending on the value is that the capacity of the small generator had already been optimized via load analysis. In the “In port” mode, efficiency improvement was obtained from a minimum of 4.5% to a maximum of 8%.
4.3. Total Cost
The more balanced the operation time of each of the four generators installed on the ship, the better. This is because the longer the operating time of the generator, the shorter its life span. If operations are biased toward one generator, maintenance becomes difficult; that is, as the total operating time of one generator increases, the maintenance cycle accelerates and the maintenance costs increase.
Table 7 lists the operating times of the small generator and large generator during the simulation. In Case 1, the operating time of the two generators is assumed to be the same because they generate the same power in this case.
In addition, the total cost owing to the fuel consumption and the operating hours of each generator can be confirmed from
Table 8. The cost of diesel fuel is 1000 USD/ton, and the lifetime of the generator is set to 15,000 (h). The capital and replacement costs are 300 USD/kW, and the operation and maintenance cost is 0.01 USD/h. Comparing the costs based on the generator capacity, we saved up to USD 230,000 compared to the existing design in 397 days. Case 6 saved 2.41%, and Case 2 saved 5.14% cost.
5. Conclusions
In this study, we presented a method for estimating the generator capacity to ensure high efficiency based on the demands of large refrigerated-container ships. First, to calculate the generator capacity, the characteristics of each operation mode were analyzed through the actual load profile data of the ship. The time ratio and power demand range for each operation mode were confirmed as quartiles of the power data for each operation mode. From the data analysis, the “At sea” mode was operated at the highest rate, and the “Port in/out” mode was operated at the lowest rate, while the required power range of each mode was the widest in the “Port in/out” mode, and the range of use was relatively narrow in the other modes. Based on this, the capacity of the small generator was calculated for the load factor of the small generator to be 80% of the median value of the required load in the “At sea” mode. To define the GCI and calculate the appropriate GCI, the efficiencies of large generators were compared based on their capacities. Following the comparison, rather than installing four generators with the same capacity, because the ratio of the two generator sets was different, the generator combination became diverse, and the efficiency increased. However, the efficiency was somewhat reduced by calculating the large generator as having twice the capacity of the small generator.
Accordingly, an appropriate capacity ratio of two generators with different capacities is required. Among the previously compared values, the one with high efficiency was selected and classified into six cases for simulation. In addition, the fuel consumption, operating time, and efficiency of the generators were compared in consideration of the set load factor and optimal combination of the PMS. We confirmed through the experiment that because the value of was small, the effect of reducing fuel consumption, increasing efficiency, and reducing the cost of the generator was remarkable. This is because the capacity of the small generator was optimized through the load analysis. In conclusion, the proposed strategy found an optimal configuration for the onboard generator capacity of the subject ship. This paper presents a method of optimizing generator capacity for a representative container ship that is currently in the trend of enlargement. The proposed strategy is simple, so it is expected that it will be applicable to various types of ships that will become larger in the future.