1. 06/2000Short-term load forecasting1 SHORT TERM LOAD FORECASTING USING NEURAL NETWORKS AND FUZZY LOGIC George G Karady Arizona State University

2. 06/2000Short-term load forecasting2 Short Term Load Forecasting Content b b Overview of Short term load forecasting Introduction Definitions and expected results Importance of Short-term load forecasting Impute data and system parameters required for load forecasting Concept Major load forecasting techniques Concept of STLF model Development b b Statistical methods (Multiply liner regression, stochastic time series e.t.c)

3. 06/2000Short-term load forecasting3 Short Term Load Forecasting Content b b Artificial Neural Networks Building block: a feed forward network Load forecasting engine Results Numerical example b b Fuzzy logic and evolutionary programming

4. 06/2000Short-term load forecasting4 Overview of Short Term Load Forecasting (STLF)

5. 06/2000Short-term load forecasting5 Introduction b b The electrical load increases about 3-7% per year for many years. b b The long term load increase depends on the population growth, local area development, industrial expansion e.t.c. b b The short term load variation depends on weather, local events, type of day (Weekday or Holiday or Weekend) e.t.c.

6. 06/2000Short-term load forecasting6 Introduction b b The building of a power plant requires: 10 years (Nuclear) 6 years (Large coal-fired) 3 years (combustion turbine) b b The electric system planing needs the forecast of the load for several years.   Typically the long term forecast covers a period of 20 years

7. 06/2000Short-term load forecasting7 Introduction b b The planning of maintenance, scheduling of the fuel supply etc. calls for medium term load forecast. b b The medium term load forecast covers a period of a few weeks.   It provides the peak load and the daily energy requirement

8. 06/2000Short-term load forecasting8 Introduction b b The number of generators in operation, the start up of a new unit depends on the load. b b The day to day operation of the system requires accurate short term load forecasting.

9. 06/2000Short-term load forecasting9 Introduction b b Typically the short term load forecast covers a period of one week b b The forecast calculates the estimated load for each hours of the day (MW). b b The daily peak load. (MW) b b The daily or weekly energy generation. (MWh)

10. 06/2000Short-term load forecasting10 Introduction b b The utilities use three types of load forecasting: Long term (e.g. 20 years) Medium term. (e.g. 3-8 weeks) Short term (e.g. one week) b b This lecture presents the short term load forecasting techniques

11. 06/2000Short-term load forecasting11 Definitions and Expected Results (Big picture) b b The short term load forecasting provides load data for each hour and cover a period of one week. b b The load data are: hourly or half-hourly peak load in kW hourly or half-hourly values of system energy in kWh Daily and weekly system energy in kWh

12. 06/2000Short-term load forecasting12 Definitions and Expected Results (Big picture) b b The short term load forecasting is performed daily or weekly. b b The forecasted data are continuously updated.   Typical short-term, daily load forecast is presented in the Table in the next page. (Salt River Project, SRP)

13. 06/2000Short-term load forecasting13 Definitions and Expected Results (Big picture) Typical short-term, daily load forecast from Salt River Project. Hourly Load in MW

14. 06/2000Short-term load forecasting14 Definitions and Expected Results (Big picture) Typical short-term, daily load forecast from Salt River Project. Hourly Load in MW

15. 06/2000Short-term load forecasting15 Importance of Short-term Load Forecasting b b Provide load data to the dispatchers for economic and reliable operation of the local power system. b b The timeliness and accuracy of the data affects the cost of operation. Example: The increase of accuracy of the forecast by 1% reduced the operating cost by L 10M in the British Power system in 1985

16. 06/2000Short-term load forecasting16 Importance of Short-term Load Forecasting b b The forecasted data are used for: Unit commitment. – –selection of generators in operation, – –start up/shut down of generation to minimize operation cost Hydro scheduling to optimize water release from reservoirs Hydro-thermal coordination to determine the least cost operation mode (optimum mix)

17. 06/2000Short-term load forecasting17 Importance of Short-term Load Forecasting b b The forecasted data are used for: Interchange scheduling and energy purchase. Transmission line loading Power system security assessment. – –Load-flow – –transient stability studies using different contingencies and the predicted loads.

18. 06/2000Short-term load forecasting18 Importance of Short-term Load Forecasting b b These off-line network studies: detect conditions under which the system is vulnerable permit preparation of corrective actions – –load shedding, – –power purchase, – –starting up of peak units, – –switching off interconnections, forming islands, – –increase spinning and stand by reserve

19. 06/2000Short-term load forecasting19 Impute Data and System Parameters for Load Forecasting b b The system load is the sum of individual load. b b The usage of electricity by individuals is unpredictable and varies randomly. b b The system load has two components: Base component Randomly variable component

20. 06/2000Short-term load forecasting20 Impute Data and System Parameters for Load Forecasting b b The factors affecting the load are: economical or environmental time weather Unforeseeable random events

21. 06/2000Short-term load forecasting21 Impute Data and System Parameters for Load Forecasting Economical or environmental factors Service area demographics (rural, residential) Industrial growth. Emergence of new industry, change of farming Penetration or saturation of appliance usage Economical trends (recession or expansion) Change of the price of electricity Demand side load management

22. 06/2000Short-term load forecasting22 Impute Data and System Parameters for Load Forecasting b b The time constraints of economical or environmental factors are slow, measured in years. b b This factors explains the regional variation of the load model (New York vs. Kansas) b b The load model depends on these slow changing factors and has to be updated periodically

23. 06/2000Short-term load forecasting23 Impute Data and System Parameters for Load Forecasting Time Factors affecting the load b b Seasonal variation of load (summer, winter etc.). The load change is due to: – –Change of number of daylight hours – –Gradual change of average temperature – –Start of school year, vacation b b Calls for a different model for each season

24. 06/2000Short-term load forecasting24 Impute Data and System Parameters for Load Forecasting Typical Seasonal Variation of Load Summer peaking utility

25. 06/2000Short-term load forecasting25 Impute Data and System Parameters for Load Forecasting Time Factors affecting the load Daily variation of load. ( night, morning,etc)

26. 06/2000Short-term load forecasting26 Impute Data and System Parameters for Load Forecasting Weekly Cyclic Variation Saturday and Sunday significant load reduction Monday and Friday slight load reduction Typical weekly load pattern:

27. 06/2000Short-term load forecasting27 Impute Data and System Parameters for Load Forecasting Time Factors affecting the load b b Holidays (Christmas, New Years) Significant reduction of load Days proceeding or following the holidays also have a reduced load. – –Pattern change due to the tendency of prolonging the vacation

28. 06/2000Short-term load forecasting28 Impute Data and System Parameters for Load Forecasting b b Weather factors affecting the load b b The weather affects the load because of weather sensitive loads: air-conditioning house heating irrigation

29. 06/2000Short-term load forecasting29 Impute Data and System Parameters for Load Forecasting Weather factors affecting the load The most important parameters are: Forecasted temperature Forecasted maximum daily temperature Past temperature Regional temperature in regions with diverse climate

30. 06/2000Short-term load forecasting30 Impute Data and System Parameters for Load Forecasting Weather Factors Affecting the Load The most important parameters are: Humidity Thunderstorms Wind speed Rain, fog, snow Cloud cover or sunshine

31. 06/2000Short-term load forecasting31 Impute Data and System Parameters for Load Forecasting Random Disturbances Effects on Load b b Start or stop of large loads (steel mill, factory, furnace) b b Widespread strikes b b Sporting events (football games) b b Popular television shows b b Shut-down of industrial facility

32. 06/2000Short-term load forecasting32 Impute Data and System Parameters for Load Forecasting b b The different load forecasting techniques use different sets of data listed before. b b Two -three years of data is required for the validation and development of a new forecasting program. b b The practical use of a forecasting program requires a moving time window of data

33. 06/2000Short-term load forecasting33 Impute Data and System Parameters for Load Forecasting b b The moving time window of data requires: Data covering the last 3-6 weeks Data forecasted for the forecasting period, generally one week

34. 06/2000Short-term load forecasting34 Impute Data and System Parameters for Load Forecasting b b The selection of long periods of historical data eliminates the seasonal variation   The selection of short periods of historical data eliminates the processes that are no longer operative.

35. 06/2000Short-term load forecasting35 Impute Data and System Parameters for Load Forecasting b b The forecasting is a continuous process. b b The utility forecasts the load of its service area. b b The forecaster prepares a new forecast for everyday and updates the existing forecast daily b b The data base is a moving window of data

36. 06/2000Short-term load forecasting36 Major Load Forecasting Techniques b b Statistical methods b b Artificial Neural Networks b b Fuzzy logic b b Evolutionary programming b b Simulated Annealing and expert system b b Combination of the above methods

37. 06/2000Short-term load forecasting37 Major Load Forecasting Techniques b b The statistical methods will be discussed briefly to explain the basic concept of the load forecasting b b This lecture concentrates on load forecasting methods using neural networks and fuzzy logic

38. 06/2000Short-term load forecasting38 Concept of STLF Model Development b b Model selection b b Calculation and update of model parameters b b Testing the model performance b b Update/modification of the model if the performance is not satisfactory

39. 06/2000Short-term load forecasting39 Concept of STLF Model Development b b Model selection Selection of mathematical techniques that match with the local requirements b b Calculation and update of model parameters This includes the determination of the constants and selection of the method to update the constants values as the circumstance varies. (seasonal changes)

40. 06/2000Short-term load forecasting40 Concept of STLF Model Development b b Testing the model performance First the model performance has to be validated using 2-3 years of historical data The final validation is the use of the model in real life conditions. The evaluation terms are: – –accuracy – –ease of use – –bad/anomalous data detection

41. 06/2000Short-term load forecasting41 Concept of STLF Model Development b b Update/modification of the model if the performance is not satisfactory Due to the changing circumstances (regional gross, decline of local industry etc.) the model becomes obsolete and inaccurate, Model performance, accuracy has to be evaluated continuously Periodic update of parameters or the change of model structure is needed

42. 06/2000Short-term load forecasting42 Artificial Neural Networks for STLF

43. 06/2000Short-term load forecasting43 Artificial Neural Networks for STLF b b Several Artificial Neural Network (ANN) based load forecasting programs have been developed. b b The following neural networks were tested for load forecasting: Feed-forward type ANN Radial based ANN Recurrent type ANN

44. 06/2000Short-term load forecasting44 Building Blocks of a Feed Forward Network b b A Feed forward Three-Layered Perceptron Type ANN was selected to demonstrate the short term load forecasting technique. b b The selected network forecasts: Hourly loads Peak load of the day Total load of the day.

45. 06/2000Short-term load forecasting45 Building Blocks of a Feed Forward Network b b The forecasting with neural network will be demonstrated using a feed forward three-layered network to forecast the peak load of the day. b b The network has: one output: (load in kW) three input: (previous day max. load and temperature, forecasted max. temperature)_

46. 06/2000Short-term load forecasting46 Building Blocks of a Feed Forward Network b b The structure of the Feed Forward Three-Layered Perceptron Type ANN is presented on the next page. b b The network contains: i = 1.. 3 input layer nodes j = 1…5hidden layer nodes k = 1 output layer nodes

47. 06/2000Short-term load forecasting47 Artificial Neural Networks for STLF

48. 06/2000Short-term load forecasting48 Building Blocks of a Feed Forward Network b b The inputs are: X 1 previous day max. load X 2 previous day max. temperature X 3 forecasted max. temperature b b W ij weight factor between input and hidden layer b b w j weight factor between hidden layer and output

49. 06/2000Short-term load forecasting49 Building Blocks of a Feed Forward Network b b A sigmoid function is placed in the nodes (neurons) of the hidden layer and output node. b b The sigmoid equation for an arbitrary Z function is: b b Youtput :maximum load

50. 06/2000Short-term load forecasting50 Building Blocks of a Feed Forward Network b b Inputs X i are multiplied by the connection weights (W ij ) and passed on to the neurons in the hidden layer. b b The weighted inputs (X i *W ij ) to each neurons are added together and passed through a sigmoid function. b b Input of hidden layer neuron 1 is:

51. 06/2000Short-term load forecasting51 Building Blocks of a Feed Forward Network  The output H j of the j hidden layer node is :  The output H j of the j th hidden layer node is :

52. 06/2000Short-term load forecasting52 Building Blocks of a Feed Forward Network b b Inputs H j are multiplied by the connection weights (w k ) and passed on to the neurons in the output layer. b b The weighted inputs (H j *w k ) to each output neurons are added together and passed through a sigmoid function.   Input of output neuron is:

53. 06/2000Short-term load forecasting53 Building Blocks of a Feed Forward Network  The output Y is :

54. 06/2000Short-term load forecasting54 Training of the Feed Forward Neural Network b b The described neural network is trained using historical data. b b Typical data set contains 2-3 years of load and weather data. b b Error back propagation (BP) method is used for the training.   During the learning the weights are adjusted repeatedly.

55. 06/2000Short-term load forecasting55 Training of the Feed Forward Neural Network b b The output produced by the ANN in response to inputs are repeatedly compared with the correct answers b b Each time the weights are adjusted slightly by beck-propagating the error at the output layer through the ANN b b Equations for the training are presented in the next page

56. 06/2000Short-term load forecasting56 Training of the Feed Forward Neural Network b b The equations used for the training are: Weight is between input and hidden layer: Weight is between hidden layer and output:

57. 06/2000Short-term load forecasting57 Training of the Feed Forward Neural Network b b In the equations: Y actual is the true value of the output load  is  learning factor (0.3-0.8) nis the number of learning cycles X j is the input value belongs to Y actual b b A numerical example demonstrates the use of neural forecasting method.

58. 06/2000Short-term load forecasting58 Training of the Feed Forward Neural Network b b The over training has to be avoided using the cross validation method: The training set is divided into two parts. (Part 1 : two years data, Part 2: one year data) Part 1 is used to train the network, by passing the data through the network. Few hundred times pass represents a training period.

59. 06/2000Short-term load forecasting59 Training of the Feed Forward Neural Network b b The over training of the network has to be avoided: Part 2 is used to check the effectiveness of the training. After each training period the error is calculated when the network is supplied by the input data of Part 2. The increase of error indicates over training, when the training has to be stopped

60. 06/2000Short-term load forecasting60 Load Forecasting Engine b b The EPRI developed a Load Forecasting Engine using 24 Neural networks. b b One network forecasts the load for each hour of the day. b b The networks are grouped into four (4) categories depending on time of the day. b b The categories have different inputs.

61. 06/2000Short-term load forecasting61 Load Forecasting Engine The construction of the engine shows the four groups of neural networks.

62. 06/2000Short-term load forecasting62 Load Forecasting Engine b b The four categories are:.Category 1. Nine neural networks. Forecasts the load between 1-9AM..Category 2. Nine neural networks. Forecasts the load between 10AM -2PM and 7 -10PM..Category 3. Four neural networks. Forecasts the load between 3-6 PM..Category 4. Two neural networks. Forecasts the load between 11-12 PM.

63. 06/2000Short-term load forecasting63 Load Forecasting Engine b b The inputs in four categories are: Category 1. Forecast for early morning – –general input – –load in the last three-four hours – –temperature in the last three-four hours Category 2. Forecast for off peak hours – –general input – –forecast temperature of previous hours – –yesterday’s load and temperature of hours close to this hours

64. 06/2000Short-term load forecasting64 Load Forecasting Engine b b The inputs in four categories are: Category 3. Forecast for afternoon peak hours – –general input – –forecast temperatures of previous and feature hours close to this hours. – –yesterday’s load and temperature of hours close to this hours Category 4. Forecast for late night hours – –general input – –forecast temperatures for the four proceeding hours

65. 06/2000Short-term load forecasting65 Load Forecasting Engine b b The general input variables are same hour load, temperature and humidity of one day ago. (3) same hour load, temperature and humidity of two days ago. (3) same hour load and temperature seven (7) days ago (2)

66. 06/2000Short-term load forecasting66 Load Forecasting Engine b b The general input variables are (continuation): same hour forecast temperature and relative humidity of the next day (2) day of the week index (Sunday 01, Monday 02 etc.)

67. 06/2000Short-term load forecasting67 Load Forecasting Engine b b The load forecasting engine has one output for the hourly load b b The extended forecast uses the forecasted values. E.g. The two-day ahead forecast uses values obtained by the one-day ahead forecast. b b The forecast can be updated each hour using the recent load and weather data

68. 06/2000Short-term load forecasting68 Load Forecasting Engine b b The weights in the neural network are adjusted daily. b b The retraining uses the actual load and weather data of the past few days. b b The retraining helps to follow the trends, changes of weather patter e.t.c

69. 06/2000Short-term load forecasting69 Load Forecasting For Holidays b b The load during the holidays has different patterns and is significantly reduced. b b The forecast is inaccurate because of the small number of historical data. b b The holiday is treated as Saturday if the shopping centers are open Sunday if the shopping centers are not open

70. 06/2000Short-term load forecasting70 Hourly Weather Forecast b b The weather service provides forecasts for: daily maximum and minimum temperature daily maximum and minimum relative humidity rain and fog maximum wind speed b b No hourly data are provided.

71. 06/2000Short-term load forecasting71 Hourly Weather Forecast b b EPRI developed an hourly temperature and humidity forecasting engine. b b Single neural network with 28 inputs : – –hourly temperature of the previous day) – –high and low temperature of the two previous day 24 outputs: expected hourly temperatures.

72. 06/2000Short-term load forecasting72 Load Forecasting Results

73. 06/2000Short-term load forecasting73 Load Forecasting Results Comparison of forecasted and actual loads

74. 06/2000Short-term load forecasting74 Load Forecasting Results Accuracy less than 3% for the next days forecast is considered good The longer term forecast accuracy is less (7-8%)

75. 06/2000Short-term load forecasting75 Appendix 1 Derivation of Learning Algorithm

76. 06/2000Short-term load forecasting76 Derivation of Learning Algorithm b The output of the hidden and output layer and the error function are:

77. 06/2000Short-term load forecasting77 Derivation of Learning Algorithm b The update of the weight factors require iteration b For the calculation of the derivative the following substitutions are used

78. 06/2000Short-term load forecasting78 Derivation of Learning Algorithm b After substitutions the equations are:

79. 06/2000Short-term load forecasting79 Derivation of Learning Algorithm  The derivation of the error function results in : b b The derivative of the u function is:

80. 06/2000Short-term load forecasting80 Derivation of Learning Algorithm b The derivative of the output function is:

81. 06/2000Short-term load forecasting81 Derivation of Learning Algorithm b The derivation of the auxiliary function Y2 gives: b The derivative of Y1 function is:

82. 06/2000Short-term load forecasting82 Derivation of Learning Algorithm b Substituting the results in the equations :

83. 06/2000Short-term load forecasting83 Derivation of Learning Algorithm b The rearrangement of the output equation results in : b The final equation for the update of dw j is:

84. 06/2000Short-term load forecasting84 Derivation of Learning Algorithm b The derivative of the hidden layer function is:

85. 06/2000Short-term load forecasting85 Derivation of Learning Algorithm b The derivation of the auxiliary function h2 gives: b The derivative of h1 function is:

86. 06/2000Short-term load forecasting86 Derivation of Learning Algorithm b Substituting the results in the equations :

87. 06/2000Short-term load forecasting87 Derivation of Learning Algorithm b The rearrangement of the output equation results in : b The final equation for the update of dW ij is:

88. 06/2000Short-term load forecasting88 Derivation of Learning Algorithm b Substituting the results in the equations which is used to iterate the w j value :

89. 06/2000Short-term load forecasting89 Derivation of Learning Algorithm b The two training algorithms are: