Title: A strategy for short-term load forecasting i n I r e l a n d Candidate: Damien Fay M.Eng. B.E. Ph.D. Thesis University Name: Dublin City University Supervisor: Marissa Condon School: Electronic Engineering Month and Year of submission: July 2004. Number of volumes: 1 ! hereby certify that this material, which I now su b m it for assessment on the programme o f study leading to the award of Ph.D. is entirely my own work and has not been taken from the work o f others save and to the extent that such work has been cited and acknowledged within the text o f my work. Sinned: f & t * ID N o : _ J ' Candidate $ Date:_ l O / e x J o i t - Acknowledgements I would like to express sincere gratitude to my supervisors Prof. John Ringwood and Dr. Marissa Condon for their patience, help and understanding over the past few years. I would also like to thank Michael Kelly and John Kennedy of Eirgrid (ESB) for their sponsorship and for providing the data and expertise to make this project possible. I would also like to thank Prof. Jerome Sheehan for his statistical expertise and advice. Finally, 1 would like to thank my parents for their endurance and Judith for her constant encouragement. Contents List Abstract 1 Chapter 1: Introduction. 2 1.1 Description of Field. 2 1.2 Motivation for Research. 5 1.3 Main thesis Contributions. 6 1.4 Thesis Structure. 8 Chapter 2: Characteristics of Irish Electrical Load Data. 10 2.1 Introduction. 10 2.2 Data Availability. 10 2.2.1 Range and Timescale o f Data. 11 2.3 Characteristics of Irish Electrical Load Data. 12 2.3.1 Trend and Variability. 12 2.3.2 Day-Types. 15 2.3.3 Temperature-Load Relationship. 17 2.3.3.1 Pre-Processing of Electrical Data to Remove Trend and Variability. 17 2.3.3.2 Pre-Processing of Temperature and Load. 20 2.3.3.3 Characterisation of the Temperature Load-Relationship. 22 2.4 Conclusion. 24 Chapter 3: A Historical Review of Approaches to Electrical Load Forecasting. 25 3.1 Introduction. 25 3.1.1 Introduction to the Load Forecasting Area. 26 3.1.1.1 Long Term Load Forecasting. 26 3.1.1.2 Medium Term Load Forecasting. 27 3.1.1.3 Short T erm Lo ad F orecasting. 27 3.2 Disaggregation Approaches in Load Forecasting. 29 3.2.1 Day-Type Disaggregation. 29 3.2.1.1 Techniques for Day-Type Identification. 3 0 3.2.1.2 Techniques for Determining the Transition between Day-Types. 33 3.2.2 Hour of the Day Disaggregation. 36 3.3 Linear Techniques for Short Term Load Forecasting. 40 3.3.1 Box-Jenkins Techniques. 41 3.3.1.1 Stationarity Transformations. 41 3.3.1.2 Model Structures. 43 3.3.1.3 Model Identification. 45 3.3.1.4 Model Estimation and Diagnostic Checking. 47 3.3.1.5 Box-Jenkins Models for Short Term Load Forecasting. 50 3.3.2 Linear State Space Techniques. 53 3.3.2.1 Kalman Filtering and State Estimation. 53 3.3.2.2 Linear State Space Model Structures. 5 7 3.3.2.3 Linear State Space Models for Short Term Load Forecasting. 60 3.3.2.4 Variance Parameter Estimation. 61 3.3.3 Bayesian Techniques. 65 3.3.4 Multi-Timescale Techniques. 66 3.3.4.1 Adaptive Scaling Techniques. 66 3.3.4.2 Murray's Multi-Timescale Technique. 69 3.4 Non-Linear Techniques for Load Forecasting. 75 3.4.1 Parametric Non-Linear Techniques. 76 ii 3.4.1.1 Wiener Models. 77 3.4.1.2 Hammerstein Models. 78 3.4.2 Fuzzy Logic Techniques. 80 3.4.2.1 Fuzzy Logic Models for Short-Term Load Forecasting. 82 3.4.2.2 Radial Basis Function Neural Networks. 85 3.4.3 Neural Network Techniques. 86 3.4.3.1 Feed Forward Neural Networks. 8 7 3.4.3.2 Recurrent Neural Networks. 92 3.5 Techniques for Integrating Weather Forecast Errors into Load Forecasts. 94 3.5.1 Techniques for Quantifying the Effect of Weather Forecast Error. 96 3.5.2 Techniques for Minimising the Effect of Weather Forecast Error. 99 3.6 Conclusion. 102 Chapter 4: Day-Type Identification. 104 4.1 Introduction. 104 4.2 Day-Type Identification. 104 4.2.1 Segmentation of Data for Model Building. Ill 4.2.2 Temperature-Load Relationship within Day-Types. 112 4.3 Transitions between Day-Types. 117 4.4 Conclusion. 121 Chapter 5: Parallel Models for Short Term Load Forecasting. 123 5.1 Introduction. 123 5.2 Construction of Partitioned Series for Parallel Model Building. 124 5.3 Examining Partitioned Series for Independence. 125 5.4 Preliminary Modelling of Partitioned Series. 127 5.4.1 Choice of Preliminary Model. 128 5.4.2 Application of the Basic Structural Model. 129 iii 5.4.2.1 Treatment of Day-Type Boundary Conditions. 131 5.4.2.2 Tuning of the Preliminary Parallel Models. 132 5.4.2.3 Tuning the Preliminary Parallel Models Using Alternative Data Partitions. 141 5.4.3 De-Seasonalisation of Weather Inputs. 143 5.5 Input Selection. 144 5.5.1 Input Reduction. 147 5.5.2 Pre-Processing and Input Selection. 149 5.5.2.1 Method 1 150 5.5.2.2 Method 2. 152 5.5.2.3 Method 3. 154 5.5.2.4 Method 4. 155 5.5.2.5 A Comparison of Methods 1-4. 156 5.6 Linear Modelling of Partitioned Series. 162 5.6.1 Input Selection and Pre-processing. 164 5.6.2 Structure Determination. 164 5.6.3 Parameter Evaluation. 164 5.6.4 Model Validation. 164 5.7 Non-Linear Modelling of Partitioned Series. 167 5.7.1 Choice of Non-Linear Model. 168 5.7.2 Input Selection and Pre-Processing. 169 5.7.3 Structure Determination. 172 5.7.3.1 Choice of Network Architecture. 172 5.7.3.2 Choice of Training Algorithm. 172 5.7.3.3 Network Topology Determination. 173 5.7.4 Parameter Evaluation. 180 5.7.5 Model Validation. 180 5.8 A Comparison of Linear and Non-linear Parallel Models. 184 5.9 Conclusion. 184 iv Chapter 6: Multi-Time Scale Modelling for Short Term Load Forecasting. 187 6.1 Introduction. 187 6.2 The Sequential Model. 189 6.2.1 Input Selection and Pre-processing. 190 6.2.2 Structure Determination. 191 6.2.3 Parameter Evaluation. 191 6.2.4 Model Validation. 192 6.3 The Cardinal Point and End-Sum Models. 201 6.4 The Multi-Timescale Model. 202 6.4.1 Weight determination: A Numerical Approach. 203 6.4.1.1 Random Weight Selection. 204 6.4.1.2 Weight Profile Selection. 204 6.4.1.3 Optimised Weight Selection. 206 6.4.1.4 Results and Analysis. 208 6.4.2 Weight Determination: A Deterministic Approach. 212 6.5 A Comparison of Parallel and Multi-Time Scale Models. 217 6.6 Conclusion. 220 Chapter 7: Fusion of Models for Load Forecasting. 223 7.1 Introduction. 223 7.2 Modelling Weather Forecast Errors. 226 7.2.1 Modelling Temperature Forecast Errors. 226 7.2.2 Modelling Cloud Cover, Wind Direction and Wind Speed Errors. 234 7.2.3 Joint Modelling of Weather Forecast Errors. 236 7.3 Choice of Load Forecasting Model. 237 7.4 Sub- Modelling of Partitioned Series. 240 7.4.1 Input Selection and Pre-Processing. 242 7.4.2 Structure Determination. 242 7.4.3 Parameter Evaluation. 243 V 7.4.4 Model Validation. 243 7.5 The Linear Model Fusion Algorithm. 244 7.5.1 Fusing Sub-Model Outputs. 245 7.5.1.1 Results without Pseudo-Weather Forecast Errors. 248 7.5.1.2 Results with Pseudo-Weather Forecast inputs. 250 7.6 The Non-Linear Model Fusion Algorithm. 252 7.6.1 Results without Pseudo-Weather Forecast Errors. 253 7.6.2 Results with Pseudo-Weather Forecast inputs. 254 7.7 Conclusion. 256 Chapter 8: Conclusions. 258 8.1 Broad conclusion. 258 8.2 Analysis of Models. 260 8.3 Recommendations and Caveats. 262 8.4 Areas for Future Research. 263 Rcferenccs. 266 Appendix A. Appendix B. vi A strategy for short-term load forecasting in Ireland. Damien Fay ABSTRACT Electric utilities require short-term forecasts of electricity demand (load) in order to schedule generating plant up to several days ahead on an hourly basis. Errors in the forecasts may lead to generation plant operation that is not required or sub-optimal scheduling of generation plants. In addition, with the introduction of the Electricity Regulation Act 1999, a deregulated market structure has been introduced, adding increased impetus to reducing forecast error and the associated costs. This thesis presents a strategy for reducing costs from electrical demand forecast error using models designed specifically for the Irish system. The differences in short-term load forecasting models are examined under three independent categories: how the data is segmented prior to modelling, the modelling technique and the approach taken to minimise the effect of weather forecast errors present in weather inputs to the load forecasting models. A novel approach is presented to determine whether the data should be segmented by hour of the day prior to modelling. Several segmentation strategies are analysed and the one appropriate for Irish data identified. Furthermore, both linear and non­ linear techniques are compared with a view to evaluating the optimal model type. The effect of weather forecast errors on load forecasting models, though significant, has largely been ignored in the literature.