Incorporating wind power forecast uncertainties into stochastic unit commitment using neural network-based prediction intervals

Penetration of renewable energy resources, such as wind and solar power, into power systems significantly increases the uncertainties on system operation, stability, and reliability in smart grids. In this paper, the nonparametric neural network-based prediction intervals (PIs) are implemented for forecast uncertainty quantification. Instead of a single level PI, wind power forecast uncertainties are represented in a list of PIs. These PIs are then decomposed into quantiles of wind power. A new scenario generation method is proposed to handle wind power forecast uncertainties. For each hour, an empirical cumulative distribution function (ECDF) is fitted to these quantile points. The Monte Carlo simulation method is used to generate scenarios from the ECDF. Then the wind power scenarios are incorporated into a stochastic security-constrained unit commitment (SCUC) model. The heuristic genetic algorithm is utilized to solve the stochastic SCUC problem. Five deterministic and four stochastic case studies incorporated with interval forecasts of wind power are implemented. The results of these cases are presented and discussed together. Generation costs, and the scheduled and real-time economic dispatch reserves of different unit commitment strategies are compared. The experimental results show that the stochastic model is more robust than deterministic ones and, thus, decreases the risk in system operations of smart grids.

Improving prediction interval quality : a genetic algorithm-based method applied to neural networks

The delta technique has been proposed in literature for constructing
prediction intervals for targets estimated by neural networks. Quality of constructed prediction intervals using this technique highly depends on neural network characteristics. Unfortunately, literature is void of information about how these dependences can be managed in order to optimize prediction intervals. This study attempts to optimize length and coverage probability of prediction intervals through modifying structure and parameters of the underlying neural networks. In an evolutionary optimization, genetic algorithm is applied for finding the optimal values of network size and training hyper-parameters. The applicability and efficiency of the proposed optimization technique is examined and demonstrated using a real case study. It is shown that application of the proposed optimization technique significantly improves quality of constructed prediction intervals in term of length and coverage probability.

Load forecasting and neural networks : a prediction interval-based perspective

Successfully determining competitive optimal schedules for electricity generation intimately hinges on the forecasts of loads. The nonstationarity and high volatility of loads make their accurate prediction somewhat problematic. Presence of uncertainty in data also significantly degrades accuracy of point predictions produced by deterministic load forecasting models. Therefore, operation planning utilizing these predictions will be unreliable. This paper aims at developing prediction intervals rather than producing exact point prediction. Prediction intervals are theatrically more reliable and practical than predicted values. The delta and Bayesian techniques for constructing prediction intervals for forecasted loads are implemented here. To objectively and comprehensively assess quality of constructed prediction intervals, a new index based on length and coverage probability of prediction intervals is developed. In experiments with real data, and through calculation of global statistics, it is shown that neural network point prediction performance is unreliable. In contrast, prediction intervals developed using the delta and Bayesian techniques are satisfactorily narrow, with a high coverage probability.

Prediction interval construction using interval type-2 fuzzy logic systems

This study proposes a novel non-parametric method for construction of prediction intervals (PIs) using interval type-2 Takagi-Sugeno-Kang fuzzy logic systems (IT2 TSK FLSs). The key idea in the proposed method is to treat the left and right end points of the type-reduced set as the lower and upper bounds of a PI. This allows us to construct PIs without making any special assumption about the data distribution. A new training algorithm is developed to satisfy conditions imposed by the associated confidence level on PIs. Proper adjustment of premise and consequent parameters of IT2 TSK FLSs is performed through the minimization of a PI-based objective function, rather than traditional error-based cost functions. This new cost function covers both validity and informativeness aspects of PIs. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Quantitative measures are applied for assessing the quality of PIs constructed using IT2 TSK FLSs. The demonstrated results for four benchmark case studies with homogenous and heterogeneous noise clearly show the proposed method is capable of generating high quality PIs useful for decision-making.

Prediction interval-based modelling of polymerization reactor: a new modelling strategy for chemical reactors

Precise and reliable modelling of polymerization reactor is challenging due to its complex reaction mechanism and non-linear nature. Researchers often make several assumptions when deriving theories and developing models for polymerization reactor. Therefore, traditional available models suffer from high prediction error. In contrast, data-driven modelling techniques provide a powerful framework to describe the dynamic behaviour of polymerization reactor. However, the traditional NN prediction performance is significantly dropped in the presence of polymerization process disturbances. Besides, uncertainty effects caused by disturbances present in reactor operation can be properly quantified through construction of prediction intervals (PIs) for model outputs. In this study, we propose and apply a PI-based neural network (PI-NN) model for the free radical polymerization system. This strategy avoids assumptions made in traditional modelling techniques for polymerization reactor system. Lower upper bound estimation (LUBE) method is used to develop PI-NN model for uncertainty quantification. To further improve the quality of model, a new method is proposed for aggregation of upper and lower bounds of PIs obtained from individual PI-NN models. Simulation results reveal that combined PI-NN performance is superior to those individual PI-NN models in terms of PI quality. Besides, constructed PIs are able to properly quantify effects of uncertainties in reactor operation, where these can be later used as part of the control process. © 2014 Taiwan Institute of Chemical Engineers.

An interval type-2 fuzzy logic system-based method for prediction interval construction

This paper introduces a new non-parametric method for uncertainty quantification through construction of prediction intervals (PIs). The method takes the left and right end points of the type-reduced set of an interval type-2 fuzzy logic system (IT2FLS) model as the lower and upper bounds of a PI. No assumption is made in regard to the data distribution, behaviour, and patterns when developing intervals. A training method is proposed to link the confidence level (CL) concept of PIs to the intervals generated by IT2FLS models. The new PI-based training algorithm not only ensures that PIs constructed using IT2FLS models satisfy the CL requirements, but also reduces widths of PIs and generates practically informative PIs. Proper adjustment of parameters of IT2FLSs is performed through the minimization of a PI-based objective function. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Performance of the proposed method is examined for seven synthetic and real world benchmark case studies with homogenous and heterogeneous noise. The demonstrated results indicate that the proposed method is capable of generating high quality PIs. Comparative studies also show that the performance of the proposed method is equal to or better than traditional neural network-based methods for construction of PIs in more than 90% of cases. The superiority is more evident for the case of data with a heterogeneous noise. © 2014 Elsevier B.V.

Prediction interval estimation for electricity price and demand using support vector machines

Uncertainty is known to be a concomitant factor of almost all the real world commodities such as oil prices, stock prices, sales and demand of products. As a consequence, forecasting problems are becoming more and more challenging and ridden with uncertainty. Such uncertainties are generally quantified by statistical tools such as prediction intervals (Pis). Pis quantify the uncertainty related to forecasts by estimating the ranges of the targeted quantities. Pis generated by traditional neural network based approaches are limited by high computational burden and impractical assumptions about the distribution of the data. A novel technique for constructing high quality Pis using support vector machines (SVMs) is being proposed in this paper. The proposed technique directly estimates the upper and lower bounds of the PI in a short time and without any assumptions about the data distribution. The SVM parameters are tuned using particle swarm optimization technique by minimization of a modified Pi-based objective function. Electricity price and demand data of the Ontario electricity market is used to validate the performance of the proposed technique. Several case studies for different months indicate the superior performance of the proposed method in terms of high quality PI generation and shorter computational times.

Prediction interval estimation of electricity prices using PSO-tuned support vector machines

Uncertainty of the electricity prices makes the task of accurate forecasting quite difficult for the electricity market participants. Prediction intervals (PIs) are statistical tools which quantify the uncertainty related to forecasts by estimating the ranges of the future electricity prices. Traditional approaches based on neural networks (NNs) generate PIs at the cost of high computational burden and doubtful assumptions about data distributions. In this work, we propose a novel technique that is not plagued with the above limitations and it generates high-quality PIs in a short time. The proposed method directly generates the lower and upper bounds of the future electricity prices using support vector machines (SVM). Optimal model parameters are obtained by the minimization of a modified PI-based objective function using a particle swarm optimization (PSO) technique. The efficiency of the proposed method is illustrated using data from Ontario, Pennsylvania-New Jersey-Maryland (PJM) interconnection day-ahead and real-time markets.

A new fuzzy-based combined prediction interval for wind power forecasting

This paper makes use of the idea of prediction intervals (PIs) to capture the uncertainty associated with wind power generation in power systems. Since the forecasting errors cannot be appropriately modeled using distribution probability functions, here we employ a powerful nonparametric approach called lower upper bound estimation (LUBE) method to construct the PIs. The proposed LUBE method uses a new framework based on a combination of PIs to overcome the performance instability of neural networks (NNs) used in the LUBE method. Also, a new fuzzy-based cost function is proposed with the purpose of having more freedom and flexibility in adjusting NN parameters used for construction of PIs. In comparison with the other cost functions in the literature, this new formulation allows the decision-makers to apply their preferences for satisfying the PI coverage probability and PI normalized average width individually. As the optimization tool, bat algorithm with a new modification is introduced to solve the problem. The feasibility and satisfying performance of the proposed method are examined using datasets taken from different wind farms in Australia.

Intervals for the assessment of measurement agreement: Similarities, differences, and consequences of incorrect interpretations

Several intervals have been proposed to quantify the agreement of two methods intended to measure the same quantity in the situation where only one measurement per method and subject is available. The limits of agreement are probably the most well-known among these intervals, which are all based on the differences between the two measurement methods. The different meanings of the intervals are not always properly recognized in applications. However, at least for small-to-moderate sample sizes, the differences will be substantial. This is illustrated both using the width of the intervals and on probabilistic scales related to the definitions of the intervals. In particular, for small-to-moderate sample sizes, it is shown that limits of agreement and prediction intervals should not be used to make statements about the distribution of the differences between the two measurement methods or about a plausible range for all future differences. Care should therefore be taken to ensure the correct choice of the interval for the intended interpretation.

Prediction interval estimation for wind farm power generation forecasts using support vector machines

Accurate forecasting of wind power generation is quite an important as well as challenging task for the system operators and market participants due to its high uncertainty. It is essential to quantify uncertainties associated with wind power generation forecasts for their efficient application in optimal management of wind farms and integration into power systems. Prediction intervals (PIs) are well known statistical tools which are used to quantify the uncertainty related to forecasts by estimating the ranges of the future target variables. This paper investigates the application of a novel support vector machine based methodology to directly estimate the lower and upper bounds of the PIs without expensive computational burden and inaccurate assumptions about the distribution of the data. The efficiency of the method for uncertainty quantification is examined using monthly data from a wind farm in Australia. PIs for short term application are generated with a confidence level of 90%. Experimental results confirm the ability of the method in constructing reliable PIs without resorting to complex computational methods.

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

Seasonal changes in pasture quality and diet selection and their relationship with liveweight gain of steers grazing tropical grass and grass-legume pastures in northern Australia.

The variation in liveweight gain in grazing beef cattle as influenced by pasture type, season and year effects has important economic implications for mixed crop-livestock systems and the ability to better predict such variation would benefit beef producers by providing a guide for decision making. To identify key determinants of liveweight change of Brahman-cross steers grazing subtropical pastures, measurements of pasture quality and quantity, and diet quality in parallel with liveweight were made over two consecutive grazing seasons (48 and 46 weeks, respectively), on mixed Clitoria ternatea/grass, Stylosanthes seabrana/grass and grass swards (grass being a mixture of Bothriochloa insculpta cv. Bisset, Dichanthium sericeum and Panicum maximum var. trichoglume cv. Petrie). Steers grazing the legume-based pastures had the highest growth rate and gained between 64 and 142 kg more than those grazing the grass pastures in under 12 months. Using an exponential model, green leaf mass, green leaf %, adjusted green leaf % (adjusted for inedible woody legume stems), faecal near infrared reflectance spectroscopy predictions of diet crude protein and diet dry matter digestibility, accounted for 77, 74, 80, 63 and 60%, respectively, of the variation in daily weight gain when data were pooled across pasture types and grazing seasons. The standard error of the regressions indicated that 95% prediction intervals were large (+/- 0.42-0.64 kg/head.day) suggesting that derived regression relationships have limited practical application for accurately estimating growth rate. In this study, animal factors, especially compensatory growth effects, appeared to have a major influence on growth rate in relation to pasture and diet attributes. It was concluded that predictions of growth rate based only on pasture or diet attributes are unlikely to be accurate or reliable. Nevertheless, key pasture attributes such as green leaf mass and green leaf% provide a robust indication of what proportion of the potential growth rate of the grazing animals can be achieved.

Use of SARIMA models to assess data-poor fisheries: a case study with a sciaenid fishery off Portugal

Research on assessment and monitoring methods has primarily focused on fisheries with long multivariate data sets. Less research exists on methods applicable to data-poor fisheries with univariate data sets with a small sample size. In this study, we examine the capabilities of seasonal autoregressive integrated moving average (SARIMA) models to fit, forecast, and monitor the landings of such data-poor fisheries. We use a European fishery on meagre (Sciaenidae: Argyrosomus regius), where only a short time series of landings was available to model (n=60 months), as our case-study. We show that despite the limited sample size, a SARIMA model could be found that adequately fitted and forecasted the time series of meagre landings (12-month forecasts; mean error: 3.5 tons (t); annual absolute percentage error: 15.4%). We derive model-based prediction intervals and show how they can be used to detect problematic situations in the fishery. Our results indicate that over the course of one year the meagre landings remained within the prediction limits of the model and therefore indicated no need for urgent management intervention. We discuss the information that SARIMA model structure conveys on the meagre lifecycle and fishery, the methodological requirements of SARIMA forecasting of data-poor fisheries landings, and the capabilities SARIMA models present within current efforts to monitor the world’s data-poorest resources.

Gestão da cadeia de abastecimento de bens de consumo baseada em modelos de previsão lineares

Dissertação apresentada ao Instituto Politécnico do Porto para obtenção do Grau de Mestre em Logística