Methodological and applicative contributions

Conclusions

60

Conclusions

61 DMs can choose any of the solutions on the Pareto front according to his / her preferences as a good compromise in terms of high PICP and low NMPIW.

 Knowledge of PIs allows the DMs and operational planners to quantify the level of uncertainty associated with the forecasts and to consider a multiplicity of solutions/scenarios for the best and worst conditions.

 We use NSGA-II, which is one of the most powerful MOEAs, for NN training. A comparison with another powerful multi-objective optimization algorithm, MO-CMA-ES, has been performed. The comparison results have shown that the PIs produced by NSGA- II are superior to those obtained with MO-CMA-ES, and satisfactory in both objectives of high coverage and small width. It is worth pointing out that it is the first time that NSGA- II is used to solve the problem for finding optimal lower and upper bounds of PIs.

 In order to show the superiority of the proposed multi-objective framework to the single- objective frameworks, particularly to the original LUBE method [36], in Paper II, we have performed comparisons on different datasets. In addition, in Paper II, we have also performed a comparison with a classical time-series regression method, i.e. ARIMA. The results confirm the superiority of our MOGA-NN approach.

Contributions with respect to the objective 2:

Objective 2: To represent the uncertainty in input data and propagate it through the prediction model onto its results.

 In order to represent the uncertainty in input data and propagate it through the prediction model onto its results, we present an interval-valued time series prediction modeling framework based on NNs [41]. With the interval-valued representation, one can reflect the variability in the inputs (e.g. extreme wind speeds in a given area, daily peak load, minimum and maximum of daily temperature, etc.), or their associated uncertainty (e.g.

strongly skewed wind speed distributions, non-stationary load patterns, etc.).

 We have presented two approaches that can be used to process interval-valued inputs to NNs, which aim at providing more accurate quantification of the input uncertainty in the prediction problem. The experiment results reveal that the interval-valued input approach is capable of capturing the variability in the input data with the required coverage. The results enable different strategies to be planned according to the range of possible outcomes within the interval forecast.

Conclusions

62

 With respect to the case study comparison results, we can conclude that our method for interval-valued day-ahead wind speed prediction performs better than the one with single- valued inputs, in that we have obtained higher quality PIs.

 Moreover, comparison results carried out between two learning algorithms, SOSA and MOGA (NSGA-II), show the superiority of the latter in training the NN in our specific problem.

Contributions with respect to the objective 3:

Objective 3: To enhance the performance of a NN-based, non-parametric prediction method by an ensemble approach.

 This objective is addressed through the introduction of a novel NN ensemble-modelling framework, by two methods to estimate PIs for short-term wind speed prediction. In the aggregation phase of the selected individual NN results, we have used k-nn approach to determine the similar patterns between training and testing sets. This allows us to obtain high accurate results also on the testing set by using the local information coming from the closest patterns of the training sets.

 Both methods demonstrate consistent results and high prediction precision compared to the individual NNs of the ensemble and to conceptually similar methods proposed in the literature [150].

 We can conclude that the NN ensemble approach proposed in Paper VII can provide a significant improvement in the quality of short-term wind speed prediction.

Contributions with respect to the objective 4:

Objective 4: To test the proposed model on real case studies in the context of energy system applications (in particular adequacy assessment).

 In Paper I, data has been obtained from experiments aimed at observing the process of deposition of the scale layer in [117], [119].

 In Papers II and III, the test of the proposed MOGA-NN approach is done on several different datasets concerning short-term wind speed and load forecasting. Wind speed datasets show different wind speed profiles with seasonality measured for the region of Regina in Saskatchewan, Canada. The first dataset comprises wind speeds for the period from 1st of February 2012 to 31st of March 2012; the second from 1st of July 2012 to

Conclusions

63 29th of August 2012; the third from 1st of February 2011 to 30th of June 2011, and the last one from 1st of May 2010 to 30th of September 2010.

 In Paper IV, the proposed method has been applied on a synthetic case study and on a real case study, in which the data show a high (short-term) variability (within hour and within day) [41]. The real case study includes the wind speed dataset which covers the period from 1^st of January 2010 till 30^th of December 2012 [123].

 In Paper V, hourly wind speed data from the region of Regina, Saskatchewan, Canada taken, from a 9-year period (1 Jan. 2003 to 31 Dec. 2011) is considered in the case study [123]. Then, hourly mean wind speed data are used to determine the time-dependent wind power output of a wind turbine generator (WTG) using its power curve. For load demand, the hourly load fluctuations are modeled using the chronological annual load curve of the IEEE Reliability Test System (RTS) [10] with the scaled annual peak load value.

 In Paper VII, the hourly wind speeds measured from 1^st of February 2003 to 28^th of July 2012 in Regina, Saskatchewan, 80000 samples in total [123].

 We can conclude that the case studies on different datasets have let us test the performance of the MOGA-NN method on various datasets having different variability.

Like all the machine learning methods, NNs have some limitations besides their advantages.

In general, NNs give high satisfactory performance in forecasting. Their capability to learn the non-linear relationship between input and output and arbitrary function mapping ability make them suitable and promising for forecasting tasks. On the other hand, NNs are data- driven and depend highly on the representativeness of the training dataset, i.e. data driven prediction methods are prone to give less accurate results depending on the high level of variability in the test set, i.e. unseen data, under consideration. Therefore, the prediction accuracy can decrease on test dataset with large variability and uncertainty in the data, with respect to the training. In other words, the difference between training and testing dataset profiles plays an important role in the generalization power of the model. Hence, a data- driven prediction method does not always guarantee to generate high quality predictions on unseen data. Moreover, a NN model can require a computationally intensive procedure for training that requires large computational times. Mostly, the computation time correlates with the network size (i.e. topology), thus the number of parameters to be optimized, and the number of training samples.

Conclusions

64 It is worth pointing out that tackling a regression problem requires also proper pre-treatment of the input data. How best to select the input variables pertinent to the output variable(s), i.e.

feature selection, for inclusion in a model is an important factor that affects both the prediction accuracy and computational cost of the underlying model. For time series forecasting, the number of the previous lags related to the output is also a key factor to be determined properly. In this thesis work, we also address these issues in our case studies, with classical techniques.