Short-term load forecasting based on a semi-parametric additive model

Short-term load forecasting is an essential instrument in power system planning, operation and control. Many operating decisions are based on load forecasts, such as dispatch scheduling of generating capacity, reliability analysis, and maintenance planning for the generators. Overestimation of electricity demand will cause a conservative operation, which leads to the start-up of too many units or excessive energy purchase, thereby supplying an unnecessary level of reserve. On the contrary, underestimation may result in a risky operation, with insufficient preparation of spinning reserve, causing the system to operate in a vulnerable region to the disturbance. In this paper, semi-parametric additive models are proposed to estimate the relationships between demand and the driver variables. Specifically, the inputs for these models are calendar variables, lagged actual demand observations and historical and forecast temperature traces for one or more sites in the target power system. In addition to point forecasts, prediction intervals are also estimated using a modified bootstrap method suitable for the complex seasonality seen in electricity demand data. The proposed methodology has been used to forecast the half-hourly electricity demand for up to seven days ahead for power systems in the Australian National Electricity Market. The performance of the methodology is validated via out-of-sample experiments with real data from the power system, as well as through on-site implementation by the system operator.Short-term load forecasting, additive model, time series, forecast distribution

Multi-task additive models with shared transfer functions based on dictionary learning

Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of these models is their interpretability: the transfer functions provide visual means for inspecting the models and identifying domain-specific relations between inputs and outputs. However, in large-scale problems involving the prediction of many related tasks, learning independently additive models results in a loss of model interpretability, and can cause overfitting when training data is scarce. We introduce a novel multi-task learning approach which provides a corpus of accurate and interpretable additive models for a large number of related forecasting tasks. Our key idea is to share transfer functions across models in order to reduce the model complexity and ease the exploration of the corpus. We establish a connection with sparse dictionary learning and propose a new efficient fitting algorithm which alternates between sparse coding and transfer function updates. The former step is solved via an extension of Orthogonal Matching Pursuit, whose properties are analyzed using a novel recovery condition which extends existing results in the literature. The latter step is addressed using a traditional dictionary update rule. Experiments on real-world data demonstrate that our approach compares favorably to baseline methods while yielding an interpretable corpus of models, revealing structure among the individual tasks and being more robust when training data is scarce. Our framework therefore extends the well-known benefits of additive models to common regression settings possibly involving thousands of tasks

Multiple linear regression and neural network for electric load forecasting

Starting from conventional models, researchers have begun to develop advanced techniques. One recent technique is the hybrid model, which improves upon the time series forecast. In this study, a hybrid model combining the multiple linear regression (MLR) model and neural network (NN) model has been developed to enhance the forecast of Malaysian short term load. Considering the data consisted of linear and nonlinear parts, it is first forecasted using the MLR model. The residuals obtained from the in-sample forecast are then forecasted using the NN model. This model has improved the forecast, although at certain hours, neural network model gives better performance. To determine the performance of the models, three performance indicators are used: root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). To assist in error measurements, we also developed a fractional residual plot to observe goodness-of-fit. A graphical plot could help an analyst see the goodness of the analysis for each of the individual data. Compared to the regular residual plot, this plot provides more information and can be used as a benchmark tool. This study also includes the missing values problem as one of the objectives. In load data, the missing problem always occurs in a set of data. Since it has a seasonal pattern according to days, most of the time, the load usage for the next day is predictable. For this reason, a new model has been developed based on these characteristics. Three imputations are tested with this method: mean (DCM1), mean + standard deviation (DCM2) and third quartile value (DCM3). The data is divided into three parts which are at the front, middle and at the end of the data with 5%, 15%, and 25% of missing values. The results of RMSE show that the proposed techniques, particularly DCM1 and DCM3, are superior to other complex methods when dealing with missing values

24-h electrical load data — a sequential or partitioned time series?

Variations in electrical load are, among other things, hour of the day dependent, introducing a dilemma for the forecaster: whether to partition the data and use a separate model for each hour of the day (the parallel approach), or use a single model (the sequential approach). This paper examines which approach is appropriate for forecasting hourly electrical load in Ireland. It is found that, with the exception of some hours of the day, the sequential approach is superior. The final solution however, uses a combination of linear sequential and parallel neural models in a multi-time scale formulation

Zonal And Regional Load Forecasting In The New England Wholesale Electricity Market: A Semiparametric Regression Approach

Power system planning, reliability analysis and economically efficient capacity scheduling all rely heavily on electricity demand forecasting models. In the context of a deregulated wholesale electricity market, using scheduling a region’s bulk electricity generation is inherently linked to future values of demand. Predictive models are used by municipalities and suppliers to bid into the day-ahead market and by utilities in order to arrange contractual interchanges among neighboring utilities. These numerical predictions are therefore pervasive in the energy industry. This research seeks to develop a regression-based forecasting model. Specifically, electricity demand is modeled as a function of calendar effects, lagged demand effects, weather effects, and a stochastic disturbance. Variables such as temperature, wind speed, cloud cover and humidity are known to be among the strongest predictors of electricity demand and as such are used as model inputs. It is well known, however, that the relationship between demand and weather can be highly nonlinear. Rather than assuming a linear functional form, the structural change in these relationships is explored. Those variables that indicate a nonlinear relationship with demand are accommodated with penalized splines in a semiparametric regression framework. The equivalence between penalized splines and the special case of a mixed model formulation allows for model estimation with currently available statistical packages such as R, STATA and SAS. Historical data are available for the entire New England region as well as for the smaller zones that collectively make up the regional grid. As such, a secondary research objective of this thesis is to explore whether or not an aggregation of zonal forecasts might perform better than those produced from a single regional model. Prior to this research, neither the applicability of a semiparametric regression-based approach towards load forecasting nor the potential improvement in forecasting performance resulting from zonal load forecasting has been investigated for the New England wholesale electricity market