Introduction to Forecasting Dr. Yogesh K. Bichpuriya TCS Research - - PowerPoint PPT Presentation
Introduction to Forecasting Dr. Yogesh K. Bichpuriya TCS Research and Innovation TATA Consultancy Services Ltd. Pune, India October 26, 2018 Yogesh Bichpuriya Introduction to Forecasting October 26, 2018 1 / 34 Menu of the day 1
TCS Research and Innovation TATA Consultancy Services Ltd. Pune, India October 26, 2018
Yogesh Bichpuriya Introduction to Forecasting October 26, 2018 1 / 34
1 Introduction 2 Load Forecasting 3 Short Term Load Forecasting
Load Profiles Forecasting Approach Case Studies
4 Other Forecasting Problems in Power Sector 5 Conclusion
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Introduction
Descriptive Analytics Predictive Analytics Prescriptive Analytics
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Introduction
(Source: Walter Baxter, geograph.org.uk)
Prediction is very difficult, especially if it’s about the future.
Physics
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Introduction
1 Important analytics for many planning and operational decision making in
Electricity sector Meteorology Supply industry Tourism sector · · ·
2 A well studied branch (and yet evolving) in econometrics, statistics and
3 One of the first papers on electrical load forecasting is by Godard
[Godard, 1955] in the year 1955.
4 Forecasting is even more important and challenging today - it stimulates
research in modeling techniques and algorithm development.
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Introduction
[Holden and Peel, 1988] summarized the process of making economic forecasts which can be extended for forecasts in general. The process includes the following.
1 Defining a causal relationship to form a model and variables to be included. 2 Selecting a functional form to represent the model. 3 Collection of the data and use it for estimating model parameters. If
estimation is not satisfactory, model specifications can be changed.
4 Forecasting of future values of the explanatory variables are determined. 5 Forecasting the variables of interest using the model. 6 The forecasts are examined and adjustments can be made to take account of
information not included in the model such as policy changes.
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Load Forecasting
Electric grid is transforming for -
Reliability Affordability Sustainability
What is changing -
Renewable Energy Targets- Solar, Wind Active Prosumers Electric Vehicles Energy Storage
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Load Forecasting
Scheduling and trading Upgradation of infrastructure to enable efficient coordination and control - to ensure reliability and resilience of the distribution system Development of distribution grid analytics - to monitor and optimize grid
Strengthen the customer facing side of the Utility to effectively manage the customers’ participation Generation reserves in case of non-availability of the green power
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Load Forecasting
Missing data and quality of data Projection of explanatory variables e.g., weather, economic indicators Impact of regulatory policies - open access in distribution system Significance of point forecasts or scenario based forecasts in long and medium term Increasing penetration of distributed energy resources (e.g., roof-top solar PV) Increasing number of electrical/electronic appliances, but more energy efficient Electric vehicles - moving and flexible loads
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Load Forecasting
Long term Medium term Short term Time hori- zon Year(s) ahead Month(s) ahead Day(s) ahead Quantity
Peak/average load in the forecasted year Hourly peak/average load
a day during a forecast month hourly/15-minutes load (load profile)
Load pro- file compo- sition Trend component Seasonal and trend components Seasonal compo- nent Important exogenous variables Economic, demo- graphic and devel-
Weather and eco- nomic indicators Day type and weather Applications Portfolio manage- ment (resource planning) and network planning Portfolio manage- ment (resource planning) Day ahead trading and scheduling
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Load Forecasting
800 1000 Hourly Maximum Load 900 950 1000 1050 Trend Component −100 100 Seasonal Component 5 10 15 20 25 30 35 40 45 −50 50 Month Index Load (in MW) Random Component
Figure: Monthly peak load of a distribution utility
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Short Term Load Forecasting Load Profiles
(a) Urban Distribustion Company (b) State Distribution Company
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Short Term Load Forecasting Load Profiles
(c) Independence Day vs Normal Day (d) Holi vs Normal Day
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Short Term Load Forecasting Load Profiles
(e) Ambedkar Jayanti (Apr. 14) (f) Maharashtra Day (May 1) (g) Terror Attack (Nov. 26, 2008) (h) Cyclone (Nov. 10, 2009)
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Short Term Load Forecasting Load Profiles
Consumer behaviour Consumer category Weather Seasonal factors Economic factors Time factors Type of day
Weekdays Weekends Holidays Social/community events - election, strike, etc.
Calamities - Natural and man-made
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Short Term Load Forecasting Forecasting Approach
Mean-Variance analysis - Coefficient of Variation Check for Stationarity Correlation study
Similar days Temperature Vs load Humidity Vs load Rainfall Vs load · · ·
Outlier/anomalous profiles detection Auto Correlation Function(ACF), Partial Auto Correlation Function (PACF) analysis · · ·
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Short Term Load Forecasting Forecasting Approach
Regression Models
Similar day approach · · ·
Time Series Models
Autoregressive (AR) Moving Average (MA) Autoregressive Moving Average (ARMA) Integrated Autoregressive Moving Average (ARIMA) Generalized Autoregressive Conditional Heteroskedastic (GARCH)
Evolutionary and Learning Models
Expert System (ES) Genetic Algorithm (GA) Particle Swarm Optimization (PSO) Fuzzy Systems (FS) Artificial Neural Network (ANN) Support Vector Machine (SVM)
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Short Term Load Forecasting Forecasting Approach
A load profile can be expressed as a linear combination of reference days’ load profiles i.e. ˆ L =
Nr
wi × Li where
Nr
wi = 1, wi ≥ 0 Nr - Number of reference days. These reference days can be selected from the historical data using following two approaches.
1 Best correlated days (Correlation coefficient of the two days’ load profiles.) 2 Least distance days (Second norm of difference vector of the two days’ load
profiles.)
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Short Term Load Forecasting Forecasting Approach
To estimate the weights wi, a Least Absolute Value (LAV) problem can be formulated as follows: min |L −
Nr
wi × Li| subject to
Nr
wi = 1 wi ≥ 0
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Short Term Load Forecasting Forecasting Approach
Assumption: The time series is stationary [Brockwell and Davis, 2008]. Autoregressive Model- AR(p) zt can be written as weighted sum of past p values of the z’s , plus an added shock at zt = φ1zt−1 + φ2zt−2 + · · · + φpzt−p + at (1) Moving Average Model-MA(q) zt can be written as weighted sum of present and past q values of the "white noise" process at zt = at − θ1at−1 − θ2at−2 − · · · − θqat−q (2) Autoregressive-Moving Average Model-ARMA(p,q) zt =φ1zt−1 + φ2zt−2 + · · · + φpzt−p + at − θ1at−1 − θ2at−2 − · · · − θqat−q
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Short Term Load Forecasting Forecasting Approach
Integrated Autoregressive-Moving Average Model-ARIMA(p,q,d)
If the series is not stationary, the series can be transformed into a stationary series by using difference operation. Differenced time series yt can be written as: yt = ▽dzt Then, yt =φ1yt−1 + φ2yt−2 + · · · + φpyt−p + at − θ1at−1 − θ2at−2 − · · · − θqat−q
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Short Term Load Forecasting Forecasting Approach
Model Identification
Mean-variance analysis Transformation- Difference operation ACF and PACF analysis
Model Estimation
Model order selection Model parameter estimation
Model checking
Residual correlations
Forecasting [Box et al., 2004]
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Short Term Load Forecasting Forecasting Approach
Selection of Inputs Preprocessing- Normalization of Inputs Multilayer Perceptron
Number of neurons in input layer Number of neurons in output layer Number of hidden layer and number of neurons in each hidden layer Activation function for each neuron, e.g. tansigmoid, logsigmoid
Objective Function-Minimization of error (SSE, MSE etc.) Learning Algorithm- e.g. Backpropagation Algo. Post Processing- getting back the values
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Short Term Load Forecasting Forecasting Approach
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Short Term Load Forecasting Forecasting Approach
Mean Absolute Error (MAE) MAE = 1 N N
|Li − Fi | Sum of Squared Error (SSE) SSE = N
2
Root Mean Squared Error (RMSE) RMSE =
N N
2
Mean Absolute Percentage Error(MAPE) MAPE % = 1 N N
|Li − Fi | Li × 100 Yogesh Bichpuriya Introduction to Forecasting October 26, 2018 25 / 34
Short Term Load Forecasting Case Studies
(i) Thursday, Jan 08, 2015 (MAPE=1.8%) (j) Wednesday, Jan 28, 2015 (MAPE=1.35%) (k) Holi, Mar 06, 2015 (MAPE=2.35%) (l) Republic Day, Jan 26, 2016 (MAPE=2.22%)
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Short Term Load Forecasting Case Studies
(m) State Discom 1 (n) State Discom 2 (o) State Discom 3 (p) Urban Discom 1
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Other Forecasting Problems in Power Sector
Many electricity markets are focusing on green energy for pollution-free electricity. The green energy sources like wind and solar are intermittent which introduces challenges for scheduling them. Renewable energy forecasting is a need to harness the potential of the wind and solar energy sources. Predicting the availability of wind and sun is difficult. Good accuracy can be achieved for shorter horizon only. Forecasting methods
Numerical weather prediction models Satellite or sky imagery based models Time series models Fuzzy logic based models · · ·
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Other Forecasting Problems in Power Sector
Important factors in wind Forecasting
Wind farm location Wind turbine characteristics
Important factors in solar and PV forecasting
System location and orientation Historical data and manufacturer specifications Forecasting for a point or for an area
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Other Forecasting Problems in Power Sector
In the electricity market with power exchange, market price is determined from the bids and offers submitted by the participants. In Locational Marginal Pricing (LMP) based markets, participants (generation and distribution companies) submit their schedules to the Market/System Operator (MO). Locational marginal prices and schedules are determined using market disptach optimization model. The spot price in electricity market depends
Demand and supply situation Network availability Demand elasticity Cost of generation (depends on fuel prices etc.) Utility function Bidding strategy
Some methods of price forecasting models the underlying process of determining price e.g., LMP.
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Other Forecasting Problems in Power Sector
In practice, an LMP based price simulation model will have to make many assumptions (bidding patterns, etc.) and will require a lot of information (network model, system conditions, etc.). Such a model will be complex and may not be necessarily efficient in terms of computational effort and time. On the other hand, a simpler model could be based on the standard time series forecasting methods like ARIMA, ANN etc. These methods model the relationship between the input (predictor) variables and the output (response) variable. These models are trained using historical data of the input and output variables. In real time, they can be used for forecasting the response variable with good accuracy.
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Conclusion
Understand the uncertainty - Probabilistic Forecast Deal with it - diversification What if we miss it - regulatory models Prepare for future
Flexibility of demand Microgrid based operation Transactive Energy
Who has seen the wind? Neither I nor you.
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Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (2004). Time Series Analysis: Forecasting and Control. Pearson Education. Brockwell, P. J. and Davis, R. A. (2008). Introduction to Time Series and Forecasting. Springer. Godard, W. W. (1955). Electrical Utility Load Forecasting [includes discussion]. Power apparatus and systems, part iii. transactions of the american institute
Holden, K. and Peel, D. A. (1988). Combining Economic Forecasts. The Journal of the Operational Research Society, 39(11):pp. 1005–1010.
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yogesh.bichpuriya@tcs.com
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