A Comparison Analysis for Optimal Controllers Based on Load Forecast Profile

The MPC and SMPC controllers require a forecast demand profile to determine the appropriate control for the ESS; Table 7-1 presents the errors for the forecast models that have been used to implement the ESS control models. We are interested in how the forecast error can affect the performance of the ESS. As discussed in the literature, an ESS control for LV network applications has typically been presented using perfect forecast models [38] [97] or forecasts with relatively small errors (between 10% to 15%) [45] [46]. Therefore, in this section, two types of forecast models, accurate and inaccurate, have been used to evaluate the proposed optimal controllers and understand the impact of forecast errors on the energy storage

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• Accurate forecasts: the future demand estimates are generated by using the most accurate forecast model, as presented in chapter 4, which only estimates the number of crane moves X₂(n), while assuming the container gross weight, X₁(n), is known in advance. This forecast has errors between 8% and 24% (from Tables 6-2 and 4-7). • Inaccurate forecasts: the future demand estimates are generated by using an inaccurate

forecast model that does not include the exogenous variable data. These give a MAPE between 21% and 39% (indicated by Table 4-7, and it generated by 5 days testing period).

The forecast models, in Table 7-1, are described in Chapter 4. In this section, the two months of collected data for the network of electrified crane demand are considered and divided into 56 days of historical data and 5 days of testing data, similar to Chapters 5 and 6. In the inaccurate forecast models, only the historical data has been used to generate the prediction profiles without requiring any of the external variables data (X₁(n) and X₂(n)). In order to use the forecast models in this section with MPC and SMPC controller, the forecast models are designed to regenerate the forecast load profile at each time step n up to a day ahead, n+ 48, by using the forecast error and actual measurements at each new time n, where the forecast model is rerun with the new observation. The forecast model output from this step will be used to operate the receding horizon controllers. The forecast results, in Table 5-1, show, that the rolling forecast models which update the model every time step significantly reduced the forecast error. In Table 7-1, the MAPE decreased to 14.2% for the ANN model (Model B.2) from 28.3% for Model (A) and to 17.2% for model (C.2) from 30.1% for the ARIMA model (Model F).

Table 7-1: The average peak demand reduction for the ESS controllers with average forecast errors.

ESS control model Accurate forecast model MAPE Peak reduction% Inaccurate forecast model MAPE Peak reduction%

MPC ANN (Model B.2) 14.2% 30.2% ANN (Model A) 28.3% 20.2%

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The test data from Chapters 5 and 6 and the main parameters of ESS in Table 6-3 have been used to operate the ESS on a network of RTG crane. The optimal controllers (MPC and SMPC) are implemented using accurate and inaccurate forecast model as shown in Table 7-1. Due to the highly stochastic nature of the crane demand and forecast errors, the ESS is unable to achieve the highest peak reduction compared to the optimal controller with perfect future demand knowledge, as seen in Figure 7-1. The SMPC outperforms all controllers except for the control model which has perfect forecasts. The receding horizon controllers with the rolling forecast model improves the performance of the ESS compared to a set-point controller, if an accurate forecast is used. In the proposed controllers with the accurate forecast models, the percentage of peak reduction, as presented in Figure 7-1 for the data given, show that the SMPC improves the performance of the ESS by increasing the peak demand reduction compared to using an inaccurate forecast. The SMPC controller achieved a 32.6% peak demand reduction compared to 30.2% for MPC, 23.9% for set-point and 36.1% for the optimal controller with a perfect load forecast. Furthermore, the ideal ESS model with infinite capacity and no limitations, where this method basically produces a flat profile, reached a highest possible peak reduction of 64.8%.

The ESS control algorithms results, shown in Figure 7-1 and Table 7-1, demonstrate that the accurate forecast models are essential for optimal controllers to maximise the energy storage performance and increase the peak demand reduction. For illustration, the percentage of peak reduction decreased to 20.2% from 30.2% for MPC and to 24.2% from 32.6% for the SMPC, when using inaccurate versus accurate forecasts respectively. While using an inaccurate forecast model for running the optimal controllers, the SMPC controller outperformed the MPC and set-point control algorithms. The stochastic algorithms allow the control model to implement an ESS plan based on a number of demand profile scenarios, which minimises the impact of the high demand volatility. Figure 7-2 presents the relationship between the forecast errors and potential peak reduction for the SMPC over the testing data period. These results show that more accurate forecasts are directly related to greater peak reductions. The forecast accuracy is a significant term and driver for potential peak reduction for optimal controllers and is more likely to achieve a high peak reduction when utilizing a more accurate forecast [149]. However, the more accurate forecast do not always guarantee the greatest peak reduction, as seen in Figure 7-2. The forecast error could be concentrated at the peak period

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rather than distributed over the day. In general, the peak demand reduction accomplished in this study will help to reduce the stress on the port’s electrical infrastructure and reduce electricity bills.

Figure 7-1:The average percentage of peak reduction for a specific case study.

Figure 7-2: The relationship between MAPE and the percentage of daily peak reduction for the SMPC controller.

The cost function aimed to reduce energy costs and create substantial reduction in the peak demand of the network of electrified RTG cranes using the electrical energy costs term and demand shaving strategy. The electricity energy tariff and the annual electricity energy cost when using accurately forecasts are presented in Chapters 5 and 6 for MPC and SMPC. Table

0% 10% 20% 30% 40% 50% 60% 70%

Set-point Optimal control with perfect forecast An ideal ESS MPC SMPC % P ea k re duc ti on Accurate forecast Inaccurate forecast 15 20 25 30 35 40 5 10 15 20 25 30 35 40 %P ea k r ed u ctio n %MAPE

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7-2 collates all the annual electricity energy cost saving for the proposed control strategies. The stochastic controller, SMPC, with accurate forecasts can achieve annual electricity bill savings of around 7.9%, near the maximum possible energy cost savings of 8.01%. The energy cost saving results, in Table 7-2, show, that the accurate forecasts improved the energy storage performance and increased the energy cost savings compared to the control models with inaccurate forecasts with an improvement of 19% on average. For example, the percentage of annual electric energy cost saving increased to 7.26% from 5.88% for MPC and to 7.98% from 6.69% for SMPC. Furthermore, the reduction of the peak demand on the electrical infrastructure (substation and cables), introduces extra economic and technical benefits. Further economic analysis for different ESS location scenarios are introduced in Section 7.2.

Table 7-2:The percentage of annual electric energy cost saving to the annual electricity energy bill.

Controller Percentage of cost saving

No forecast/ perfect forecast Accurate Inaccurate

Set-point 5.47 - -

Optimal controller with perfect forecast 8.01 - -

MPC - 7.26% 5.88%

SMPC - 7.98% 6.96%

As presented in Figure 7-1, all proposed optimal controllers which have an accurate forecast outperform the benchmark, set-point controller. Due to the highly stochastic demand behaviour and the peak demand distributed over the 24 hours a day, the set-point controller usually depletes the stored energy quickly at insignificant peak points. The substation is then forced to feed the network of cranes rather than utilize the ESS. The resulting improvement for optimal controllers is due to the penalty's for high energy costs at peak demand. Furthermore, the MPC and SMPC models allow for the minimisation of the maximum demand during the single electricity tariff period which helps to increase the peak reduction even more. The MPC and SMPC controllers, with rolling forecast and control models will also increase the robustness of the controllers by better reacting to the most recent demand changes. In the following subsection, new data sets from accurate forecast models were used to evaluate the proposed controller performance.

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