Energy Storage Management of Maritime Grids
6.4 Typical Problems
6.4.1 Energy Storage Management in AES for Navigation Uncertainties
Fig. 6.12 Power demand curves for a port crane [13]
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 137 (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:
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 opti- mized 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 real- ized. 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.
Pre-voyage Intra-voyage
t=6
t=0 t=12 t=18 t=24
...
Half-hour
Short-term navigation uncertainty characterization Second Stage: On-lin
recourse actions Pre-voyage navigation uncertainty
characterization First stage: Optimal shipborad microgrid
operation for the worst navigation uncertainty case
Fig. 6.13 Relation between the first and second stage of proposed model, reprinted from [33], with permission from IEEE
0 5 10 15 20 25 Time Step ( t)
0 5 10 15 20 25
Crusing speed (knot)
20 25 30 35 40 45 50
EEOI (gCO2/nmton)
Method A:
speed
Method B:
First-stage speed Method B:
Second-stage speed Method A:
EEOI
Method B:
First-stage EEOI Method B:
Second-stage EEOI
Fig. 6.14 Cruising speed and EEOI comparisons. Reprinted from [33], with permission from IEEE
(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.
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.
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.
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 Typical Problems 139
180 182 184 186 188 190 192 194 196 198 200 202
Voyage distance (nm) 0
10 20 30 40 50 60
Frequency (times)
Method A Method B: first stage Required
terminal distance:
188.8nm
Fig. 6.15 On-time rates of robust and non-robust models. Reprinted from [33], with permission from IEEE
Fig. 6.16 Multi-battery ESS scheme in first and second stages. Reprinted from [33], with permission from IEEE
0 5 10 15 20 25
Time Step ( t) -15
-10 -5 0 5 10
Multi-battery ESS power (MW)
-15 -10 -5 0 5 10 15
Multi-battery ESS SOC(MWh)
First-stage power Second-stage power First-stage SOC Second-stage SOC