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Modeling Electricity Demand: A Neural Network Approach

28 th Annual IAEE International Conference June 6, 2005, Taipei, Taiwan. Modeling Electricity Demand: A Neural Network Approach. Christian Crowley GWU Department of Economics. Support. This study is part of a larger joint effort supported by a EPA STAR grant:

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Modeling Electricity Demand: A Neural Network Approach

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  1. 28th Annual IAEE International Conference June 6, 2005, Taipei, Taiwan Modeling Electricity Demand: A Neural Network Approach Christian Crowley GWU Department of Economics

  2. Support This study is part of a larger joint effort supported by a EPA STAR grant: “Implications of Climate Change for Regional Air Pollution and Health Effects and Energy Consumption Behavior” Co-researchers in the project are • Frederick Joutz from the George Washington University Department of Economics • Benjamin Hobbs and Yihsu Chen from the Johns Hopkins University Department of Geography and Environmental Engineering • Hugh Ellis from the Johns Hopkins University School of Public Health “ANN Electricity Modeling.” Crowley, GWU.

  3. Outline • Context of the Research • Introduction to ANN Modeling • Basics of Electricity Demand • Developing the Demand Model • Results “ANN Electricity Modeling.” Crowley, GWU.

  4. I. Context of the Research “ANN Electricity Modeling.” Crowley, GWU.

  5. Context The modeling efforts of the STAR grant are • Electricity load modeling and forecasting • … • … • … “ANN Electricity Modeling.” Crowley, GWU.

  6. Context The modeling efforts of the STAR grant are • Electricity load modeling and forecasting • Electricity generation and dispatch modeling • … • … “ANN Electricity Modeling.” Crowley, GWU.

  7. Context The modeling efforts of the STAR grant are • Electricity load modeling and forecasting • Electricity generation and dispatch modeling • Regional air pollution modeling • … “ANN Electricity Modeling.” Crowley, GWU.

  8. Context The modeling efforts of the STAR grant are • Electricity load modeling and forecasting • Electricity generation and dispatch modeling • Regional air pollution modeling • Health effects characterization “ANN Electricity Modeling.” Crowley, GWU.

  9. II. Intro to ANN Modeling “ANN Electricity Modeling.” Crowley, GWU.

  10. ANN Model Architecture Independent Variables Dependent Variables ANN “ANN Electricity Modeling.” Crowley, GWU.

  11. ANN Model Architecture Input Layer Output Layer “ANN Electricity Modeling.” Crowley, GWU.

  12. ANN Model Architecture “ANN Electricity Modeling.” Crowley, GWU.

  13. ANN Model Architecture Elements of a neuron “ANN Electricity Modeling.” Crowley, GWU.

  14. ANN Model Architecture Elements of a neuron • Multiplicative Weight (w) “ANN Electricity Modeling.” Crowley, GWU.

  15. ANN Model Architecture Elements of a neuron • Multiplicative Weight (w) • Additive Bias (b) “ANN Electricity Modeling.” Crowley, GWU.

  16. ANN Model Architecture Elements of a neuron • Multiplicative Weight (w) • Additive Bias (b) • Transfer Function ( f ) “ANN Electricity Modeling.” Crowley, GWU.

  17. ANN Model Architecture Elements of a neuron • Multiplicative Weight (w) • Additive Bias (b) • Transfer Function ( f ) The Neuron uses these elements in its operation, when it receives an input (p) and produces a result (a) “ANN Electricity Modeling.” Crowley, GWU.

  18. ANN Model Architecture Once a neuron receives an input (p), the neuron’s operation consists of two parts: “ANN Electricity Modeling.” Crowley, GWU.

  19. ANN Model Architecture Once a neuron receives an input (p), the neuron’s operation consists of two parts: • Linear Transformation using the weight (w) and bias (b) “ANN Electricity Modeling.” Crowley, GWU.

  20. ANN Model Architecture Once a neuron receives an input (p), the neuron’s operation consists of two parts: • Linear Transformation using the weight (w) and bias (b) • Application of the Transfer Function ( f ) “ANN Electricity Modeling.” Crowley, GWU.

  21. ANN Model Architecture Once a neuron receives an input (p), the neuron’s operation consists of two parts: • Linear Transformation using the weight (w) and bias (b) • Application of the Transfer Function ( f ) The neuron then passes the result (a) on to the next part of the ANN. “ANN Electricity Modeling.” Crowley, GWU.

  22. ANN Model Architecture Linear Transformation • Multiply the input (p) by a weight (w) and add the bias (b) to get the intermediate result (n): “ANN Electricity Modeling.” Crowley, GWU.

  23. ANN Model Architecture Linear Transformation • Multiply the input (p) by a weight (w) and add the bias (b) to get the intermediate result (n): n = w x p + b “ANN Electricity Modeling.” Crowley, GWU.

  24. ANN Model Architecture Linear Transformation • Multiply the input (p) by a weight (w) and add the bias (b) to get the intermediate result (n): n = w x p + b • Pass the intermediate result (n) to the transfer function “ANN Electricity Modeling.” Crowley, GWU.

  25. ANN Model Architecture Transfer Function • Apply the transfer function ( f ) to the intermediate result (n) to create the neuron’s result (a) “ANN Electricity Modeling.” Crowley, GWU.

  26. ANN Model Architecture Transfer Function • Apply the transfer function ( f ) to the intermediate result (n) to create the neuron’s result (a) • For neurons in the input layer, the transfer function is typically a hard-limiting switch at some threshold, say n = 0: f(n) = (0 for n≤ 0; 1 for n > 0) “ANN Electricity Modeling.” Crowley, GWU.

  27. ANN Model Architecture Transfer Function • Apply the transfer function ( f ) to the intermediate result (n) to create the neuron’s result (a) • For neurons in the input layer, the transfer function is typically a hard-limiting switch at some threshold, say n = 0: f(n) = (0 for n≤ 0; 1 for n > 0) • For neurons in the output layer, the “pure linear” transfer function typically has no effect: f(n) = n “ANN Electricity Modeling.” Crowley, GWU.

  28. ANN Model Architecture “ANN Electricity Modeling.” Crowley, GWU.

  29. ANN Model Architecture “ANN Electricity Modeling.” Crowley, GWU.

  30. ANN Model Architecture “ANN Electricity Modeling.” Crowley, GWU.

  31. ANN Model Architecture “ANN Electricity Modeling.” Crowley, GWU.

  32. ANN Model Architecture Example: A Neuron’s Operation • Say a neuron has a weight of 10, a bias of 100, and a hard-limiting transfer function with a threshold of n = 0: w = 10; b = 100 f(n) = (0 for n≤ 0; 1 for n > 0) “ANN Electricity Modeling.” Crowley, GWU.

  33. ANN Model Architecture Example: A Neuron’s Operation • Say a neuron has a weight of 10, a bias of 100, and a hard-limiting transfer function with a threshold of n = 0: w = 10; b = 100 f(n) = (0 for n≤ 0; 1 for n > 0) • Say the neuron receives an input of 5: p = 5 “ANN Electricity Modeling.” Crowley, GWU.

  34. ANN Model Architecture Example: A Neuron’s Operation • Say a neuron has a weight of 10, a bias of 100, and a hard-limiting transfer function with a threshold of n = 0: w = 10; b = 100 f(n) = (0 for n≤ 0; 1 for n > 0) • Say the neuron receives an input of 5: p = 5 • The neuron’s linear transformation produces an intermediate result of 150: n = 10 x 5 + 100 = 150 “ANN Electricity Modeling.” Crowley, GWU.

  35. ANN Model Architecture Example: A Neuron’s Operation • Say a neuron has a weight of 10, a bias of 100, and a hard-limiting transfer function with a threshold of n = 0: w = 10; b = 100 f(n) = (0 for n≤ 0; 1 for n > 0) • Say the neuron receives an input of 5: p = 5 • The neuron’s linear transformation produces an intermediate result of 150: n = 10 x 5 + 100 = 150 • The neuron’s transfer function produces the neuron’s result of 1: a = f(n) = 1 “ANN Electricity Modeling.” Crowley, GWU.

  36. ANN Model Architecture “ANN Electricity Modeling.” Crowley, GWU.

  37. ANN Model Selection • The weights and biases are determined by the ANN during training “ANN Electricity Modeling.” Crowley, GWU.

  38. ANN Model Selection • The weights and biases are determined by the ANN during training • Training involves presenting the ANN with input-output examples “ANN Electricity Modeling.” Crowley, GWU.

  39. ANN Model Selection • The weights and biases are determined by the ANN during training • Training involves presenting the ANN with input-output examples • Training is finding the weights and biases that minimize the performance function “ANN Electricity Modeling.” Crowley, GWU.

  40. ANN Model Selection • The weights and biases are determined by the ANN during training • Training involves presenting the ANN with input-output examples • Training is finding the weights and biases that minimize the performance function • The performance function is typically some measure of model error, such as MSE “ANN Electricity Modeling.” Crowley, GWU.

  41. ANN Model Selection To build an ANN, the researcher specifies • the number of layers • Input • Output • Hidden (if any) “ANN Electricity Modeling.” Crowley, GWU.

  42. ANN Model Selection To build an ANN, the researcher specifies • the number of layers • Input • Output • Hidden (if any) • the number of neurons in each layer • typically 1-5 input neurons • typically 1 output neuron “ANN Electricity Modeling.” Crowley, GWU.

  43. ANN Model Selection To build an ANN, the researcher specifies • the number of layers • Input • Output • Hidden (if any) • the number of neurons in each layer • input layer: typically 1-5 neurons • output layer: typically 1 neuron • the type of transfer function for each neuron • input layer: typically hard-limiting (0-1 switch) • output layer: typically pure-linear (no effect) “ANN Electricity Modeling.” Crowley, GWU.

  44. ANN Model Selection The researcher specifies • the number of layers • Input • Output • Hidden (if any) • the number of neurons in each layer • input layer: typically 1-5 neurons • output layer: typically 1 neuron • the type of transfer function for each neuron • input layer: typically hard-limiting (0-1 switch) • output layer: typically pure-linear (no effect) • the performance function for the network (MSE) “ANN Electricity Modeling.” Crowley, GWU.

  45. III. Basics of Electricity Demand “ANN Electricity Modeling.” Crowley, GWU.

  46. Electricity Demand • Utilities are interested in forecasting peak demand “ANN Electricity Modeling.” Crowley, GWU.

  47. Electricity Demand • Utilities are interested in forecasting peak demand • Peak demand determines how many generators the utility must bring on line “ANN Electricity Modeling.” Crowley, GWU.

  48. Electricity Demand • Utilities are interested in forecasting peak demand • Peak demand determines how many generators the utility must bring on line • Overestimating demand is costly “ANN Electricity Modeling.” Crowley, GWU.

  49. Electricity Demand • Utilities are interested in forecasting peak demand • Peak demand determines how many generators the utility must bring on line • Overestimating demand is costly, wasteful • Underestimating peak leads to electricity shortfalls “ANN Electricity Modeling.” Crowley, GWU.

  50. Electricity Demand Hourly peak electricity demand depends on • Weather • … • … • … • … “ANN Electricity Modeling.” Crowley, GWU.

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