Enhanced Classification with Logistic Regression for Short Term Price and Load Forecasting in Smart Homes (Technical Report for MSCS Course: Research Methodology in Information Technology RMIT CUI Fall 2018 9 ) Javaria Hameed, Nadeem Javaid* Department of Computer Science, COMSATS University, Islamabad 44000, Pakistan {javariahameed43, nadeemjavaidqau}@gmail.com *Correspondence:
[email protected], www.njavaid.com
Abstract—In this paper, accurate electricity load and price forecasting is achieved. To achieve this, a new system model has been proposed, which consists of feature engineering and classification. To remove irrelevant features, Decision Tree (DT) and Recursive Feature Elimination (RFE) is used. Then, features are extracted through Mutual Information (MI) after removing uncertainty. In order to attain accurate electricity load and price forecasting, Enhanced Logistic Regression (ELR) classifier is proposed. Simulation results testify that accuracy of ELR is better than Logistic Regression (LR) and MultiLayer Percepton (MLP). ELR beats LR and MLP by 0.26% and 7.287% in load forecasting whereas, it outperforms LR and MLP in price forecasting by 1.413% and 3.057% respectively. Smart* dataset is used, which contains the data of residential sector of Western Massachusetts. Prediction performance is evaluated by using MAE, MSE, RMSE and MAPE. Index Terms—Smart grid, Load and price forecasting, Enhanced LR, Feature Selection, Classification, Forecasting
I. I NTRODUCTION
TABLE I L IST OF A BBREVIATIONS Abbreviations DNN DTC ELR LR LSTM MAE MAPE MI MKELM MLP MSE RFE RMSE RNN SG SVM SVR WNN
Full Form Deep Neural Network Decision Tree Classifier Enhanced Logistic Regression Logistic Regression Long-Short Term Memory Mean Absolute Error Mean Absolute Percentage Error Mutual Information Multi Kernel Extreme Learning Machine MultiLayer Precepton Mean Squared Error Recursive Feature Elimination Root Mean Square Error Recurrent Neural Network Smart Grid Support Vector Machine Support Vector Regression Wavelet Neural Network
With the increase in world population, the demand for energy is also increasing simultaneously. It is estimated that world TABLE II population will grow to 9.8 billion by 2050 from 7.6 billion in L IST OF S YMBOLS 2017. 40 percent of global energy is consumed by residential Symbols Description and commercial buildings [1]. So, energy is one of the most Av Actual Value valuable asset. Utilities distribute electricity to the homes by Fv Forecasted Value grids. Traditionally, utilities operate through manual exchange of data by one-way communication. Traditional system are incapable of dealing with increased demand, as most of them are outdated. It results to the interruption in transmission. control their electricity bills by adjusting the timings and usage So, to utilize energy efficiently, concept of smart grids and of electricity. It allows consumer to view real-time energy use. smart houses is introduced. Smart grid is the modern system Moreover, smart meters allow companies to grant consumers that includes “two-way” communication [2], which enables with an incentive to efficiently manage energy consumption and save money. Most of the time precise and exact price consumers1 and utilities to track energy data in real-time. 2 Smart grid is an advanced and efficient system that helps forecasting is anticipated. Customers actually wants to know to detect and fix interruptions in transmission. It also helps whether the electricity price excel the threshold. So, they can in reducing electricity theft. It enables users to monitor and decide to turn on and off the load [3] . 1 Consumers,
Customers and Users are used interchangeably.
2 Prediction
and forecasting is used alternatively.
Fig. 1. Proposed System Model
Power companies can gain profits and cost of electricity can be reduced with the exact forecasting of price. It facilitates in balancing power consumption and generation. Hence, accurate load and price forecasting is vital for both utilities and users. Data analytics plays an essential role in smart grid, which enables hour-ahead, day-ahead and even month-ahead accurate forecasting achievable. Data analytics involves descriptive, prescriptive and predictive analysis. However, the main focus in this paper is on predictive analysis. In literature, there are many techniques for price and load prediction. In this paper, Logistic Regression (LR), Multilayer Precepton (MLP) and Enhanced Logistic Regression (ELR) is used for short-term forecasting of electricity load and price. The main objective of this work is to propose a model that can perform accurately and efficiently, which will minimize the cost for consumers. The organization of rest of the paper is: Section 2 consists of related work whereas, proposed system model is discussed in section 3. Section 4 comprises of simulations and results. Section 5 and 6 contains performance evaluation and conclusion.
A. Motivation Following is the motivation for this paper: •
•
•
•
Price and load forecasting is performed in various research in past however, there are limited literature in which both short-term price and load are predicted together in a single research. Mutual Information (MI) is used for feature extraction according to relevancy as in [4]. It helps in reducing the uncertainty between the features and target variable. Two-stage feature selection is performed to remove the redundancy of data. Decision Tree Classifier (DTC) and Recursive Feature Elimination (RFE) is used, which helps to reduce dimensionality. Features having minor effect on target will be removed whereas, features with more value will be selected. In the end, only those features will be passed to classifier that helps in maximizing the training speed and improving accuracy of model. LR is used for prediction. It fits the model and predict the output [5]. MLP is also used for prediction in this paper.
B. Problem Statement In [5], accuracy was calculated with the help of LR. LR was used in one of the layers of model with CNN and Adam optimizer. However, the focus of [5] was on appliances. So, in this paper, accuracy of electricity load and price prediction will be calculated by ELR. ELR is an enhanced version of LR. With the help of ELR, an accurate and cost-effective model is being proposed for both price and load forecasting. This technique outperforms LR and MLP on the basis of accuracy. C. Contribution In this paper, load and price forecasting is performed. The objective of work is to predict efficient results that will help in minimizing the cost and improving the accuracy of model. To achieve this objective, ELR has been used as a classifier. ELR measures relationship between one dependent variable (label) and one or more independent variables (features) to get the prediction. Following are main contribution of this paper: • A system model has been proposed. Feature selection, extraction and classification has been integrated to reach to the prediction of price and load. • Best features are selected on the basis of importance by combining DTC and RFE. RFE reduces the redundancy from features. • To implement this model, MI is used for feature extraction. They are extracted on the basis of ‘amount of information’. Features that are fit for the model are then passed to classifier. • ELR is used for forecasting. Prediction is performed on testing data and day-ahead load and price is forecasted. Parameters are adjusted to improve the accuracy of model. • Proposed model performs better than LR and MLP. Performance is then evaluated by RMSE, MAPE, MAE and MSE. II. R ELATED W ORK There are several forecasting techniques that are present in the literature from classical to data mining techniques. In literature, price and load are forecasted separately most of the time. In general, there are three types of forecasting techniques: classical, data driven and artificially intelligent techniques. Classical methods include Naive Bayes, Random
TABLE III
S UMMARY OF R ELATED W ORK Techniques used Deep-RNN [6]
Objectives Load forecasting
Data Set Irish
Limitation Outfitting problem
LSTM based RNN [7]
Load forecasting
University and Airline passenger
Can perform only on univariate data
CNN-Kmean [8]
Load forecasting
Industry
Setting values of parameters not discussed
Quantile Smoothing [9] Spline Regression Simple Moving Average [10] +Random Forest MKELM [11]
Load forecasting
SENSIBLE
No feature selection
Load forecasting
Korea Electricity Power Company
Peak loads need to be manage
Price forecasting
PJM, Ontario, New South Wales
Redundancy problem
Bayesian [12]
Behavioral Load forecasting
UK-Dale
Refinement of model required for multiple houses
GELM-WNN [13]
Probabilistic Load forecasting
AEMO, ISES
Redundant features not removed
SVR [14]
Day-Ahead Load forecasting
State Grid Corporation of China
Only single building type involved
Bayesian [15]
Load forecasting
Pacific NorthWest National Lab
Redundancy not removed
DNN-LSTM [16]
Price and Load forecasting
ISO-NE
Issue of redundancy
ELM [17]
Price forecasting
Swedish MCP
Underlying model not fit
SVR [18]
Load forecasting
Irish CER
Feature Redundancy
DNN [19]
Load forecasting
Macedonian hourly electricity consumption dataset
Only Single Customer
Forest, ARIMA etc. Support Vector Machine (SVM), Decision part of European project SENSIBLE. It was evaluated using ´ Tree, Neural Network and Naive Bayes are traditional classifiers. a real-life test case dataset in Evora, Portugal. This model Artificial intelligent methods includes Artifical Neural Network, provides a reliable forecast. Deep Neural Network (DNN), Shallow Neural Network etc. In [10], university campus dataset has been taken for shortIn paper [6], Deep Recurrent Neural Network (Deep-RNN) term electric load prediction. Moving average and Random is used for forecasting load. The key challenge in this study was Forest are used as 2-stage classifier, that outperforms SVR to overcome uncertainties in high volatility of load. Overfitting and ANN. The limitation in this work is with the peak challenges that were there in naive deep network was solved load management. Multi Kernel Extreme Learning Machine in [6]. To overcome the overfitting problem further network (MKELM) is used for price forecasting [11] on PJM dataset. size of the model is to be extended. Computational stability was solved in this paper. Experimental To forecast load, Long-Short Term Memory (LSTM) based results proved that it outperformed ELM and KELM models. RNN technique is implemented in [7]. In short-term forecasting, However, data redundancy is not discussed in this paper. accuracy is one of the biggest goal. So to achieve this goal, Bayesian network prediction is used to predict behavioral RNN and LSTM are combined here to perform better and load forecasting. Short-term, long-term and even seasonal accurate result. It has been proved that LSTM-based forecasting forecasting is discussed here. However, it is not efficient as outperformed conventional prediction methods. The limitation refinement of model is required for multiple houses [12]. Realin this work is that this model can only perform on univariate time prediction will be performed that will help utilities after data. refinement of model. SG enables to find trend of load and cost. It gives help In paper [13], a novel method has been used for electricity to utility to make a supply and maintenance plan. Feature load prediction which includes Wavelet Neural Network engineering is an essential part in data analytics. There are (WNN). It removes uncertainties from the model and is different papers in which authors have not discussed about implemented on Ontario and Australian electricity market data. feature redundancy. In [8], hourly load has been predicted with An ELM based methods that can be used on multi-layer network CNN and K-mean. The experimental result shows that the is to be performed in future. proposed method outperform LR, CNN and SVR. However, In [14], hybrid SVR model is used to predict the hourly setting values of parameters are not discussed. electricity load demand in a hotel building with and without the Quantile Smoothing Spline Regression is used in [9] for Multi resolution Wavelet Decomposition. Only single building forecasting of day-ahead load. The model used in [9] is the type was involved in [14]. The model learns dependency
without any preceding knowledge in [15], where bayesian network model is used for load prediction. The model was used to assess the consumption behavior of users effected by pricing policies. Paper [16] focuses on DNN-LSTM for price and load forecasting focusing on energy price trends and consumption behavior. It helps in improving market operations planning. Extreme Learning Machine (ELM) network is proposed in [17] for price prediction. Limitation of this paper is that underlying technique is not fit and different feature sets and real-time datasets are required for better performance. In [18], [19] load forecasting is performed by SVR and DNN respectively. In [19], weather data is also required to find the strength of deep learning algorithms in load prediction. Medium-term and long-term prediction also needed to be discussed. III. P ROPOSED S YSTEM M ODEL A new system model is proposed to attain the accurate load and price forecasting in Smart Homes to minimize cost and increase efficiency. The proposed system model comprises of 4 steps: preprocessing of data, training and testing of data, and forecasting using test data. Proposed system model is shown in figure 1. A. Preprocessing of Data Daily system load data is acquired from the UMass Smart* Home Dataset. The goal of Smart* project is to efficiently manage home energy consumption. It contains real time, high resolution dataset from different houses. Power data collected from a real home G over a period of 15 days (1/1/2016 15/1/2016) is utilized in this paper. The dataset contains hour wise data. The appliance-level power consumption values have been collected with varying measurement samples in each household. Hence, dataset contains different kinds of values (such as float values) which are not accepted by DT Classifier. Therefore, normalization of data is must to ensure that the complied data has same sampling and there are no errors during the compilation. B. Training and Forecasting of Data After preprocessing, data is split into testing and training. Model is trained on training data whereas, testing data is used for accurate and efficient forecasting of price and electricity load. In the end, performance evaluation is performed by Mean Absolute Percentage Error (MAPE), Mean Square Error (MSE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). C. Framework The issue of load and price prediction is to get accurate and cost-effective results. To improve the accuracy, a system model has been proposed that consists of DTC and RFC for feature selection, MI for feature extraction and ELR for prediction. Following are the parts of proposed framework: • To predict the accurate load and price of smart homes, important features are to be selected. Features are selected
•
•
on the basis of importance by DTC with respect to the target variable. To reduce the dimension and redundant features, RFE technique is applied till relevant features are selected. RFE chooses the best or worst performing features. After the feature selection, MI is used to reduce the uncertainty of features. It reduces the uncertainty about features on the basis of target. High MI indicates that particular feature is important for the target and will effect the accuracy if it is not selected. At last, features having highest value of importance and high effect on target variables are selected. Then, the best features are given to the forecasting engine for prediction. None of those features are selected that have zero effect on the target variable.
IV. S IMULATIONS AND R ESULTS Simulations are performed on the system Intel core i3, 4GB RAM and 500 GB storage. Simulations results are as follow. A. Dataset Description Daily system load is acquired from the dataset - the Smart*. This dataset is taken from UMass Trace Repository online. Smart*, an open dataset, supports research on forecasting power demands. It contains real time, high resolution dataset from different houses. It includes home electricity consumption at 1-hour intervals. The electricity price data used in simulations are taken from Massachusetts Electricity Company. It operates the generation and transmission system of Western Massachusetts. B. Feature Selection using DTC and RFE DTC and RFE is applied to calculate the importance of features with respect to target. A total of 13 features are passed for feature selection. Two-stage feature selection is used to remove the redundancy of data. Features are selected on the basis of importance in DT classifier. DTC finds the feature ranking. Fig. 2 and 3 shows the importance of features for price and load data, respectively. Algorithm 1 Algorithm of RFE 1: Begin 2: F eature ← read dataset, 3: Split 0 F eature0 ← T raining (0.75%) & T esting (0.25%) 4: Train the model on training set using all predictors 5: Calculate variables dimensions 6: Calculate rankings 7: Keep the subset predictors Si , f or most important 8: End Then, to further reduce the dimension and redundant features, RFE technique is applied till relevant features are selected. RFE chooses the best or worst performing features. The main purpose of RFE is selection of features by recursively considering subsets. RFE uses fit function to remove recursion and to calculate accuracy. RFE is used to reduce nonlinear dimension.
2.0
Fig. 2. Feature Importance using Decision Tree Classifier for Price
PGR outlets
Kitchen outlets 5
Range oven
Kitchen outlets 4
Kitchen outlets 3
Guest room outlets
Ejector pump
Variable
Fig. 4. Feature Importance using Mutual Information for Price
0.4
2.0
Fig. 3. Feature Importance using Decision Tree Classifier for Load
C. Feature Extraction using MI
Variable
PGR outlets
Kitchen outlets 5
Kitchen outlets 4
Range oven
Guest room outlets
Office outlets 1
Kitchen outlets 3
Ejector pump
Kitchen outlets 2
Kitchen outlets 1
PGR outlets
Kitchen outlets 5
Kitchen outlets 4
Range oven
Kitchen outlets 3
Guest room outlets
Office outlets 1
Ejector pump
Kitchen outlets 2
0.0
Kitchen outlets 1
0.0
Water pump
0.5
Gen
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Water pump
1.0
Gen
0.2
1.5
Kitchen microwave
Importance
0.3
Kitchen microwave
Importance
Office outlets 1
PGR outlets
Kitchen outlets 5
Kitchen outlets 4
Range oven
Guest room outlets
Office outlets 1
Kitchen outlets 3
Ejector pump
Kitchen outlets 2
Kitchen outlets 1
Water pump
0.0
Kitchen microwave
0.0
0.5
Kitchen outlets 2
0.1
1.0
Water pump
0.2
1.5
Kitchen outlets 1
0.3
Kitchen microwave
Feature Importance
Importance
0.4
Fig. 5. Feature Importance using Mutual Information for Load
the binary classification. Output is determined on the basis To reduce the uncertainty of data, Generalized MI is used. of one or more independent features. It helps in predicting It finds the mutual dependence between the two variables. MI a binary outcome. It is a predictive analysis that describes between the joint disturbance and target feature is useful for the relationship between dependent (target) and independent the feature extraction. So, variables are extracted on the basis (features) variables. This relationship is measured by estimating of relevancy of features with the target in feature extraction. probabilities by using logistic function. The candidate predictor Fig. 4 and 5 shows the importance of features for price and variables do not have to be normally distributed and equal variances. They can be continuous or discrete. Features that load data on the basis of MI, respectively. are selected in preprocessing, are normalized and weights are D. Forecasting added. Then, activation function is added. If there are errors, Data are split in training and testing, in which training and then the process is again repeated. LR is standard in packages testing hours are 270 and 90. This data is given to forecasting like SAS, STATA, R, Python and SPSS. Figure 6 shows the structure of LR. engine for prediction as shown in table 4. After the feature engineering process, relevant features are Since LR is mostly used in classification. So, to improve the sent to the ELR Classifier. ELR is basically enhanced version prediction calibration of parameters is performed. To minimize of LR. LR model is basically a linear model. It is one of the error and reduce chances of overfitting, value of ‘C’ has
700
TABLE IV T RAIN T EST S PLITTING Test 90
Price ($/MWh)
Train 270
500
Actual Prediction
500 400
400 300
Load (MW)
200 20
300 200
40
Hours
60
80
Fig. 7. ELR Price Prediction of 90 hours
20
40
Hours
60
80
Fig. 6. ELR Load Prediction of 90 hours
Actual Prediction
500 400
Load (MW)
100
Actual Prediction
600
300
been decreased. By changing the value of ‘C’, accuracy is improved in ELR. Forecasted load and price of 90 hours of January 2016 are shown in figure 6 and 7, respectively. There is a variation in load and it has been observed that maximum load is utilized during day time. Highest load is observed at 10 hours as shown in figure 9. Forecasted load and price of 1 day of January 2016 are shown in figure 8 and 9, respectively. Figure 10-13 shows comparison of forecasted load and price by different techniques and enhanced technique. It shows that enhanced technique performs better than other techniques.
Algorithm 2 Algorithm of LR 1: Begin 2: Input V ariables ← read dataset, 3: Split 0 F eature0 ← T raining (0.75%) & T esting (0.25%) 4: C ← 1.0 5: Intercept Scaling ← 1 6: M ax Iter ← 100 7: V erbose ← 0 8: n jobs ← 1 9: M LP.f it(F eature T rain, Label T rain) 10: P rediction ← M LP.predict(F earure T est) 11: End
200 100
5
10
Hours
15
20
Fig. 8. ELR Load Prediction of 1 Day
Enhanced LR accuracy for load and price was 84.0704 and 90.8025 respectively. This accuracy was more than LR and MLP accuracy as shown in table 5.
Algorithm 3 Algorithm of ELR 1: Begin 2: Input V ariables ← read dataset, 3: Split 0 F eature0 ← T raing (0.75%) & T esting (0.25%) 4: C ← 0.5 5: Intercept Scaling ← 1.5 6: M ax Iter ← 105 7: Random State ← 42 8: verbose ← 1 9: N jobs ← 4 10: M LP.f it(F eature T rain, Label T rain) 11: P rediction ← M LP.predict(F earure T est) 12: End
700
Actual Prediction
Price ($/MWh)
600
2500
Price ($/MWh)
2000
500
1500
400
1000
300
500
200 5
10
Hours
15
0
20
30
40
50
Hours
60
70
Actual LR MLP Enhanced
350 300
Load (MW)
Load (MW)
400
20
400
Actual LR MLP Enhanced
500
10
Fig. 11. Comparison of different techniques on Price
Fig. 9. ELR Price Prediction of 1 day
250
300
200
200 100
Actual LR MLP Enhanced
150 100 10
20
30
40
Hours
50
60
70
Fig. 10. Comparison of different techniques on Load
V. P ERFORMANCE E VALUATION For performance evaluation, four evaluation indicators are used:Mean Absolute Percentage Error (MAPE), Mean Square Error (MSE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). MSE has low error value than MSE and RMSE as shown in figure 14, 15 and table 6.
5
10
Hours
15
20
Fig. 12. Comparison of different techniques on Load(One Day)
The formulas of MSE, MAE , RMSE and MAPE is given in equation 1, 2 ,3 and 4. PN M AE =
n=1
|(Fv − Av )| N
TM 1 X (Av − Fv )2 T tm=1 v u TM u1 X RM SE = t (Av − Fv )2 T tm=1
M SE =
M AP E =
TM 1 X Av 100| | T tm=1 Fv
(1) (2)
(3)
(4)
VI. C ONCLUSION In this paper, short-term price and load forecasting is done.The proposed forecast model includes data cleansing, feature engineering and ELR classifier and forecasting of 24 and 72 hours load and price data. With the help of MI, DTC
TABLE VI P ERFORMANCE E VALUATORS FOR ELR
Actual LR MLP Enhanced
450
Price ($/MWh)
400 350
Evaluator MSE MAE RMSE MAPE
300
Value (Load) 0.4882 1.800 3.305 15.930
Value (Price) 0.56540 1.916 3.3820 9.197
250 200 5
10
Hours
15
20
Fig. 13. Comparison of different techniques on Price(One Day)
TABLE V ACCURACY OF L OAD AND P RICE F ORECASTING Accuracy LR MLP ELR
Load (%) 83.8105 76.7873 84.0704
Price (%) 89.3892 87.7455 90.8025
and RFE features are selected. After selection of features, prediction is performed by ELR. Prediction accuracy of ELR is compared with other popular models. Experimental results testify that proposed ELR outperforms LR and MLP. ELR beats LR and MLP by 0.26% and 7.287% in load forecasting whereas, it outperforms LR and MLP in price forecasting by 1.413% and 3.057% respectively. This model was evaluated using Smart* dataset. In the future, other methods can be used to improve the forecasting accuracy.
Error Value
20
150
LR MLP ELR
15 10 5 0 MAE
MSE
RMSE
MAPE
Fig. 14. Load Performance Evaluators
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LR MLP ELR
15.0
Error Value
12.5 10.0 7.5 5.0 2.5 0.0 MAE
MSE
RMSE
MAPE
Fig. 15. Price Performance Evaluators
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