Dr SN Singh, Professor Department of Electrical Engineering. Indian Institute of Technology Kanpur

Transcription

1 Short Term Load dforecasting Dr SN Singh, Professor Department of Electrical Engineering Indian Institute of Technology Kanpur

2 Basic Definition of Forecasting Forecasting is a problem of determining the future values of a timeseries from current and past values. Past measurements Forecasted values one step ahead two step ahead Multiple step ahead Time sampling can be in sec, min, hours, days, months and years Short term forecast Medium term forecast Long term forecast

3 Role of Forecasting in Electric Power System Before Deregulation of Electric Power System Only Load Demand forecasting is carried Economic operation and Unit commitment Maintenance and planning of power system After Deregulation of Electric Power System Monopolistic Deregulated Market Motivation: Creating competition among the suppliers Leaving choices to the buyers

4 Role of Forecasting in Electric Power System.Contd. Electricity Market Operation GENCO s/suppliers Energy, Ancillary Services, and Transmission Forecasting Load Day ahead Price Wind Power Hour ahead Bids Bids Bidding Bidding strategies/risk strategies/risk Management Management Schedules Real Time Markets Shdl Schedules ISO s Market Forecast Load Price Market Operation SCUC A S Auction Cong. Mgmt. Trans. Pii Pricing

5 Market Bidding Process Day ahead bidding for day 2 Hour ahead bidding for day 2 Day 1 Real Day 2 time Market clearing for day 2 Day ahead Forecast (24+6hrs)

6 Important Tools 1. Load Forecast 2. Price Forecast 3. Operating Reserve Margin Forecast 4. Wind Forecast System Operator Point of View: Planning Problems: Due to uncertainty, unlike conventional generators, wind power generation cannot be included into ELD and UC problems. Operational: Frequency control, Voltage control, Power Quality, Ancillary services provision. Wind power producer point of view: Bidding in dayahead, adjustment andsettling Electricity Markets to maximize profits/minimize their imbalance costs.

7 Factors Influencing the Forecast Variable Time Factor Hour in a day Day of the Week Holiday Load Demand Type of Customer Domestic loads Commercial loads Industrial loads Weather Parameters Temperature Humidity Sky cover Sun shine Wind Speed & Direction

8 Effect of Time Factor x Load Dem mand (MW) First Week Second Week Time sample

9 Dependency on Weather Parameter: Temperature Temp ( o C) Loa ad Demand (MW) 5 x Time sample Load Demand (MW) x Temp ( o C)

10 Factors Influencing Electricity Market Price Load Demand Network Congestion Electricity Market Clearing Price Reserve Margin Fuel Prices Available Hydro Generation

11 Price vs. Load Demand load demand (MW W) time samples (hrs) MC CP ($/MWh) ) Market Clea aring price ($/MWh time samples (hrs) MCP ($/MWh) load demand (MW) time samples (hrs)

12 Factors Influencing Wind Power Generation Wind Speed Wind Power Wind Direction Wind Turbine Layout Terrain

13 Wind Speed (m m/s) Wind Power (MW) Wind speed and wind power time series x Time sample x 1 4

14 Wind Speed vs. Wind Power scatter plot Win nd Power (MW) Wind Speed (m/s)

15 Forecasting Approaches Linear Regression Models : The forecast value is linearly dependent on the past historical values of the time series. (AR, ARMA, ARIMA, GARCH, etc.) AR(p): Autoregressive model of order p ARMA(p,q): Autoregressive Moving Average model of order (p,q). MA(q): Moving Average model of order q Generalized AutoRegressive Conditional Heteroskedasticity (GARCH)

16 The general process for a GARCH model involves three steps. The first is to estimate a best-fitting autoregressive model; secondly, compute autocorrelations of the error term and lastly, test for significance. GARCH models are used by financial professionals in several arenas including trading, investing, hedging and dealing.

17 Forecasting Approaches (Contd..) ARIMA: Autoregressive Integrated Moving Average Model ARIMA is a generalized form of ARMA model. It is applied when time series has some non stationary behavior (do not vary about a fixed mean). Fractional ARIMA: Thistypeof modelsareemployed employed when time series exhibits long memory. F ARIMA model is a special case of ARIMA(p,d,q) process. Where parameter d assumes fractionally continuous values in the range (.5,.5).

18 Correlation Analysis Finding the appropriate values of p and q can be facilitated by Partial Auto Correlation Functions (PACF) and Auto Correlation Functions (ACF). If Mean of a Time series is given : and Variance is given by : Then auto correlation at lag k is given by :

19 Example in Matlab : AR(1) 1 AR(1): x t = x t-1 +e, with =.8 8 e=randn(1,1); x=zeros(1,1); x(1)=e(1); 5 alpha=.8; for i=2:1 x(i)=alpha*x(i 1)+e(i); end subplot(3,1,1) plot(x); title('ar(1): x_{t}=\alpha{x_{t 1}+e}, with \alpha{=.8}'); subplot(3,1,2); autocorr(x,25,[],2); subplot(3,1,3); parcorr(x,25,[],2); AR( (1) ACF PACF Lag Lag

20 Example in Matlab : AR(2) 1 AR(2): x t = 1 x t x t-2 +e, with 1=1.5, 5 2 =-.75 e=randn(1,1); 5 x=zeros(1,1); x(1)=e(1); x(2)=e(2); alpha1=1.5; alpha2 =.75; -5 for i=3:1, x(i)=alpha1*x(i -1 1)+alpha2*x(i 2)+e(i); end subplot(3,1,1) plot(x); title('ar(2): x_{t}=\alpha_{1}x_{t 1}+\alpha_{2}x_{t {t 2}+e, with \alpha{1}=1.5, \alpha_{2}=.75'); subplot(3,1,2); autocorr(x,25,[],2); subplot(3,1,3); parcorr(x,25,[],2); A R(2) ACF Lag 1 PACF Lag

21 Example in Matlab : MA(1) 4 MA(1): x t = x t-1 +e, with =.8 e=randn(11,1); 2 theta=.8; x=e(2:11,1) theta*e(1:1,1); -2 subplot(3,1,1) plot(x); title('ma(1): x_{t}=\theta{x_{t 1}+e}, with \theta{=.8}'); subplot(3,1,2); autocorr(x,25,[],2); subplot(3,1,3); parcorr(x,25,[],2); MA(1) ACF Lag 1.5 PACF Lag

22 Example in Matlab : MA(2) 5 MA(2): x t =e t - 1 e t-1-2 e t-2 e=randn(12,1); theta1= 1.5; theta2=.8; x=e(3:12,1) theta1*e(2:11,1) theta2*e(1:1,1); subplot(3,1,1); plot(x); title('ma(2): x_{t}=e_{t} \theta_{1}e_{t 1} \theta_{2}e_{t 2} ); subplot(3,1,2); autocorr(x(2:end),2,[],2); subplot(3,1,3); parcorr(x(2:end),2,[],2); 2); ) MA(2 ACF PACF Lag Lag

23 Example in Matlab : ARMA(2,1) clear all; close all; e=2*randn(3,1); x=zeros(3,1); x(1)=e(1); x(2)=e(2); alpha1=.9; alpha2 =.3; 3 theta1=.5; for i=3:3 x(i)=alpha1*x(i 1)+ () ( ) alpha2*x(i 2)+ e(i) theta1*e(i 1) ; end subplot(3,1,1) 1) plot(x); subplot(3,1,2); autocorr(x(25:end),3,[],2); subplot(3,1,3); parcorr(x(25:end),3,[],2); ) ARMA(2,1 ACF PACF Lag Lag

24 ACF and PACF for casual Time series models AR(p) MA(q) ARMA(p,q) ACF Tails off Cuts off after lag q Tails off PACF Cuts off after lag p Tailsoff Tailsoff

25 Estimation of Model Parameters After choosing p and q the model can be fitted by linear least squares regression to find the model parameters which minimize the error terms.

26 Consider a univariate AR(p) process: State-Space Models This could be written in state-space form as, state equation observation equation

27 Limitations of Linear Regression Models As they are linear models, they cannot capture the non linear relation between the independent and dependent variable. The forecasting error increases rapidly with the increase in lookahead time. The model parameters have to be updated very frequently.

28 Forecasting Approaches..contd Non Linear Regression models: Artificial Neural Networks (ANN): are well established in function approximation, many variants of NNs are employed in the field of forecasting problem. Like FFNN, RNN, RBF, WNN. Network Parameters + Back Propagation Algorithm, Evolutionary based Optimization methods like GA, PSO are also applied for network training. Input variables are selected using ACF and PACF.

29 Other Methods.. Fuzzy Logic Adaptive Neuro Fuzzy Inference System (ANFIS) Dt Data Mining i techniques like clustering and Support Vector Machines (SVM) based classification and Regression models Wavelet pre filtering based ANN and Fuzzy models.

30 Benchmark Models

31 Then, Measure of Errors

32 AWNN : Architecture

33 Continuous Wavelet Transforms A wavelet is a small wave which grow and decays essentially in a limited time period. Should satisfy two basic properties and

34 Training Algorithm

35 Case study: Load Forecasting Load Dema and (MW) 3.5 x ACF Lag.5 PACF Lag

36 Cross correlation between Load and Temp. 5 x 14 Load (MW) Tem mp ( C) XCF Lag

37 Input lag hours selected for Load Forecasting Load Terms Temp. Terms Temp. time series Load time series Epochs: (input, output) pairs

38 AWNN

39 x 14 Hour ahead load forecast Load Dem mand (MW) Hour =.695

40 Loa ad Demand (MW) 24 hours ahead dforecast x 14 Sat Sun Mon Tue Wed Thu Fri Sat Sun time samples Forecast hour MAPE Average

41 Case study: Price Forecasting 3 MC CP ($/MWh) time samples (hrs) ACF Lag MCP ($/MWh) time samples (hrs)

42 3 25 MCP ($/MWh) load demand (MW) time samples (hrs) time samples (hrs) 1 Price Terms Load Terms.5 XCF Lag

43 Price Forecasting Results 2 1 hr ahead Price Forecast (MAPE = ) Forecast hour MAPE MCP ($/MWh) MCP ($/MW Wh) time samples (hrs) hr ahead Price Forecast time samples (hrs) Average

44 Wind Speed Time Series 25 2 wind sp peed time samples 2 wind spe eed time samples

45 Schematic Block Diagram for Wind Speed Forecasting

46 Multiresolution Analysis of Wind Speed Time Series S7 D7 D6 D5 D4 D3 D2 D1 wind Series time (hours)

47 ACF s of Decomposed Wind Speed Time Series 1 S7-1 1 D7-1 1 D6-1 1 D5-1 1 D4-1 1 D3-1 1 D2-1 1 D Lag

48 Network Architecture and Input Lag Hours Decomposed Input Lag hours NetworkArchitecture Signal AWNN FFNN S7 1 14, , , , D7 1 12,76 83, D6 1 1,41 44, D5 1 6,21 23, D4 1 3,11 13,23 25,48, D3 1,2,5,6,12,6, D2 3,6,9, D1 1,2,5,

49 Wind Power Forecast Wind Speed highly stochastic random non stationary. Wind Farm speed Wind rated speed Cut in speed Manufacturer curve Wind Power outp put

50 Wind Power Forecasting: Time Horizon Very Short Term Forecasting : Up to 2 3 h in steps of 1min. or 15min. Turbine control Real time participation in electricity market. Short Term Forecasting : Up to 24h in steps of 1h. Hour ahead bidding Intraday market Day ahead market Unit commitment and Economic dispatch Ancillary services management Day ahead reserve setting Medium Term Forecasting ( With NWP inputs): up to 72h in steps of 1h. In addition to the above mentioned benefits Maintenance planning of wind farms Wind farm and storage device Coordination Congestion management Maintenance planning of network lines. 5

51 Wind Power Forecasting: Approaches 1) NWP forecasts Physical Model Wind Speed at Hub height WP Forecast Manufacturer curve NWP forecasts 2) Wind speed Wind power Statistical Model WP Forecast Available historical measurements. ARX, ARMAX, NN, Fuzzy, ANIF

52 A Two stage approach for Wind Power Forecast Historical measurements of wind speed. AWNN Wind speed forecasts Wind speed Wind power FFNN WP Forecast

53 Autocorrelation Analysis of Wind Series la tio n p le A u to c o rre Sam n A utocorrelatio Sample Sample Autocorrelation Function Sample Autocorrelation Lag Function Lag Samp le A utoc orrela tion n S a m p le A utocorrelatio Sample Autocorrelation Function Sample Autocorrelation Lag Function Lag

54 Hour Ahead Forecast of Wind Speed 12 1 wind sp peed 8 AWNN 6 FFNN Actual hours

55 3 hours ahead Wind Speed Forecast actual forecast by AWNN forecast by FFNN wind spee ed (m/s) time (hours)

56 Comparative Performance 4.5 errors MAE of AWNN MAE of FFNN MAE of NR MAE of PER RMSE of AWNN RMSE of FFNN RMSE of NR RMSE of PER look-ahead time (hours)

57 Percentage Improvement per rcentage imp provement MAE over PER RMSE over PER MAE over NR RMSE over NR look-ahead time (hours)

58 Wind speed to Wind Power Transformation Wind Forecasted speed wind speed FFNN Wind power wind power Forecast FFNN Inputs: wind speed {, 1, 2} lag hours and from wind power series {1, 2, 3, 4, 5, 6} lag hours.

59 Error Distributions and Forecasting Ability Occurence e of errors(%) ce of errors(% %) Occuren Error(% of P inst ) 1 hr ahead forecast error distributions Error(% of P inst ) inst 3 th hr ahead forecast error distributions margin(%) hin the error of tim es wit % % 12.5% look-ahead time (hours)

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