A Comparative Study of Optimal Energy Management Strategies for Energy Storage with Stochastic Loads
Abstract
:1. Introduction
 Conventional or traditional controllers such as setpoint controller and proportional integral (PI): this type of storage controllers is limited to a specific target or reference value. These controllers generate control decisions based on a determined target or reference value such as current, energy level and voltage. The reference value is determined based on an a priori network data together with domainexpert knowledge. Due to the simplicity of these conventional controllers, they have been widely used in RTG crane systems with storage devices for reducing gas emissions and peak demand [5,6,7,8]. Furthermore, the setpoint controller is also used as a standard benchmark control system for an ESS in LV applications [9] and RTG cranes [2]. However, these controllers are principally limited for controlling volatile and nonsmooth demands, solving complex energy problems and targeting the energy savings and peak reduction over long periods of time such as an entire day. In addition, the setpoint and PI controllers are sensitive to the setpoint and use no knowledge of the potential future demand.
 Optimal controllers: this energy control category can be further divided into optimal controllers that use, or do not use, forecast of the demand. Both controllers in this category work to find the optimal (the best) ESS operation plan based on the parameters and limitations of the electrical network and storage device [10,11]. However, the optimal controllers are more complex, with higher computational costs, compared to the conventional controllers [11,12]. While many papers have discussed and investigated optimal energy control strategies for LV demands such as residential customers, there is limited literature on using these strategies for reducing peak demand or energy costs for RTG crane networks. In 2017, PenaBello et al., presented an optimisation operation algorithm for a battery storage system for gridconnected housing with a PV system [13]. The model in [13] assumed a perfect forecast for the residential load and PV generation, which is unrealistic in practice. The research does not consider the impact of forecast error or the variability of the PV generation on the operational model and results. The literature [13,14,15] has shown that accurate forecasts are important to optimise the control of an ESS. The literature has introduced the optimal control of ESS with load forecasts as a key feature for improving the peak reduction and the cost savings. However, it has widely focused on developing different planning, operation schedules based on full future knowledge to increase the energy savings by assuming a perfect forecast for the residential load and PV generation [13], which is unrealistic in practice and assumes that the charged energy was fixed and equal to a specific magnitude in [16].
 Firstly, we develop three predictive optimal controllers (MPC, SMPC and optimal controller with fixed forecast) for an ESS within an RTG crane network and compare the corresponding ESS performance. The comparison in this paper investigates the stability and robustness of the proposed controllers by using different forecast models and data sets to test the proposed ESS controllers. This evaluation is significant to understand the impact of forecast errors on the ESS control algorithms and due to the limited literature on developing predictive control algorithms for stochastic load, such as RTG crane demand.
 Secondly, unlike the limited literature [10,11], which do not investigate the complexity and computational cost of the predictive control model, this paper analyses the ESS performance by taking into consideration the main characteristics of the proposed optimal energy controllers. The analysis in this paper aims to introduce an initial assessment of the complexity for a practical implementation of the proposed optimal control systems.
2. RTG Cranes and ESS Models Topology
 Four gantry motors to move the crane around the site.
 Hoist motor to raise container weights of up to 40 tones.
 Two trolley motors to move the hoisting unit across the span of the crane.
3. The Electrified RTG Crane Demand
 Overview of the electrified RTG crane demand;
 Time series analysis.
3.1. Overview of the Electrified RTG Crane Demand
3.2. Time Series Analysis
 Accurate forecasts: the half hourly demand for the next 48time steps are generated by using the most accurate forecast model with the mean absolute percentage error (MAPE) forecast errors between 8% and 24%, as presented in [3]. This forecast model estimates the number of RTG moves, while assuming the container gross weight is known in advance.
4. Optimal Energy Controllers for RTG Crane Network
 1
 Optimal energy controller with a fixed load forecast profile: a 24 hahead RTG crane demand forecast and electricity price data are fed into the optimal control system. The control model will be updated once every 24 h. As discussed previously, the RTG crane demand profile is volatile and nonsmooth; therefore, developing an optimal controller for an RTG crane network is difficult and challenging [3,10].
 2
 Model Predictive Controller: the MPC aims to minimise the peak demand and electricity cost by finding the optimal ESS output and using a rolling forecast model to predict the RTG cranes demand. In this control model, the rolling forecasting minimises the impact of forecast error within the day on the ESS performance compared to the previous model with fixed load forecasts. However, in realistic scenarios, the RTG crane demand profile includes a high level of uncertainty. For example, the crane electrical demand is quite variable even when the RTG is lifting the same container gross weight [3,11], and this is mainly due to the human behavioural element (crane operator) during the lifting mode. The container gross weight and numbers of crane moves is used in [3] as input variables for the RTG demand forecast model.
 3
 Stochastic Model Predictive Controller: the SMPC is designed to handle the diverse and high level of uncertainty of the RTGs demand and the rolling forecast error. The SMPC aims to solve the RTG crane energy optimisation problem under the uncertainty conditions for the forecast demand. In this paper, the future crane demand is modelled as a stochastic variable by generating several future profiles, which is in contrast to the singlepoint forecast profile used in the MPC model [11].
4.1. Optimal Energy Controller with a Fixed Load Forecast Profile
4.2. Model Predictive Controller
Algorithm 1: Basic concept of MPC for RTGs network with storage device. 

4.3. Stochastic Model Predictive Controller
5. Results and Discussion
 Optimality for peak demand reduction and cost saving: the following section compares and evaluates the potential peak reduction and cost saving results for the predictive controllers (SMPC and MPC) with different levels of forecast accuracy, the setpoint controller and the optimal energy controller model with perfect forecast profiles. In order to evaluate the predictive controllers, two future demand profiles from accurate and inaccurate forecast models have been used. This evaluation is significant in understanding the impact of forecast errors on the ESS control algorithms.
 Complexity and computational cost: Section 5.2 presents indicators regarding the complexity of a practical implementation of the predictive optimal controllers.
5.1. Analysis of Energy Storage Control Strategies
Results and Discussion for Optimal ESS Controllers
5.2. Complexity and Computational Cost
SMPC and the Computational Effort
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviation
RTG  Rubber tyre gantry 
MPC  Model predictive control 
SMP  Stochastic model predictive control 
ESS  Energy storage system 
LV  Low voltage 
MV  Medium voltage 
PI  Proportional integral 
PoF  Port of Felixstowe 
ARIMAX  Autoregressive integrated moving average with explanatory variable 
SoC  State of charge 
$\mathrm{P}\left(\mathrm{t}\right)$  Power demand (RTG crane) 
$\mathrm{D}\left(\mathrm{t}\right)$  Power grid at time t 
$\widehat{\mathrm{P}}\left(\mathrm{t}\right)$  Estimated crane demand at time t 
$\Delta \mathrm{E}\left(\mathrm{t}\right)$  The stored energy in the ESS at time t 
${\mathrm{SoC}}^{\mathrm{max}}$  Greatest stored energy 
${\mathrm{SoC}}^{\mathrm{min}}$  Lowest stored energy 
$\mathrm{Cost}\left(\mathrm{t}\right)$  Represent the realtime electricity cost at Port of Felixstowe 
Cost_{day}  The electricity price during daytime (07:00 to 24:00) 
Cost_{night}  The electricity price during nighttime (24:00 to 7:00) 
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ESS Control Model  Accurate Forecast Model  MAPE  Peak Reduction%  Inaccurate Forecast Model  MAPE  Peak Reduction% 

MPC  ANN (Model B)  14.2%  30.2%  ANN (Model A)  28.3%  20.2% 
SMPC  ARIMAX (Model C)  17.2%  32.6%  ARIMA (Model D)  30.1%  24.2% 
Controller  Percentage of Cost Saving  

No Forecast/Perfect Forecast  Accurate  Inaccurate  
Setpoint  5.47     
Optimal controller with perfect forecast  8.01     
MPC    7.26%  5.88% 
SMPC    7.98%  6.96% 
Number of Forecast Demand Scenarios  Average Simulation Duration (s)  Maximum Simulation Duration (s) 

5  11  25 
10  21  33 
15  36  49 
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Alasali, F.; Haben, S.; Foudeh, H.; Holderbaum, W. A Comparative Study of Optimal Energy Management Strategies for Energy Storage with Stochastic Loads. Energies 2020, 13, 2596. https://doi.org/10.3390/en13102596
Alasali F, Haben S, Foudeh H, Holderbaum W. A Comparative Study of Optimal Energy Management Strategies for Energy Storage with Stochastic Loads. Energies. 2020; 13(10):2596. https://doi.org/10.3390/en13102596
Chicago/Turabian StyleAlasali, Feras, Stephen Haben, Husam Foudeh, and William Holderbaum. 2020. "A Comparative Study of Optimal Energy Management Strategies for Energy Storage with Stochastic Loads" Energies 13, no. 10: 2596. https://doi.org/10.3390/en13102596