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An Innovative Model Based on FCRBM

for Load Forecasting in the Smart Grid

Ghulam Hafeez1,2, Nadeem Javaid1(B

), Muhammad Riaz2, Khalid Umar3,

Zafar Iqbal4, and Ammar Ali1

1COMSATS University Islamabad, Islamabad 44000, Pakistan

nadeemjavaidqau@gmail.com

http://www.njavaid.com

2University of Engineering and Technology, Mardan 23200, Pakistan

3Bahria University Islambad, Islamabd 44000, Pakistan

4PMAS Agriculture University, Rawalpindi 46000, Pakistan

Abstract. In this paper, an eﬃcient model based on factored condi-

tional restricted boltzmann machine (FCRBM) is proposed for electric

load forecasting of in smart grid (SG). This FCRBM has deep layers

structure and uses rectiﬁed linear unit (RELU) function and multivari-

ate autoregressive algorithm for training. The proposed model predicts

day ahead and week ahead electric load for decision making of the SG.

The proposed model is a hybrid model having four modules i.e., data

processing and features selection module, FCRBM based forecaster

module, GWDO (genetic wind driven optimization) algorithm-based

optimizer module, and utilization module. The proposed model is exam-

ined using FE grid data of USA. The proposed model provides more

accurate results with aﬀordable execution time than other load fore-

casting models, i.e., mutual information, modiﬁed enhanced diﬀerential

evolution algorithm, and artiﬁcial neural network (ANN) based model

(MI-mEDE-ANN), accurate fast converging short term load forecasting

model (AFC-STLF), Bi-level model, and features selection and ANN-

based model (FS-ANN).

1 Introduction

Electric load forecasting is an indispensable decision-making tool for energy man-

agement in both sectors of SG i.e., supply side and demand side. It also plays

an important role in the secure and economic operations of SG [1]. Keeping

aforesaid objectives the recent research in SG focus load scheduling based on

optimization techniques [2,3]. However, the accuracy of electric load forecast-

ing models is compromised due to their inﬂuence on stochastic factors such as

climate change, human social activates, and country policies. Consequently, it

is diﬃcult to improve the forecast accuracy and hardly realistic to take all the

inﬂuencing factors into account [4]. Thus, an intelligent model is required that

intelligently take the key parameters to improve forecast accuracy.

c

Springer Nature Switzerland AG 2020

L. Barolli et al. (Eds.): IMIS 2019, AISC 994, pp. 49–62, 2020.

https://doi.org/10.1007/978-3-030-22263-5_5

50 G. Hafeez et al.

Numerous models have been proposed and applied for an accurate load fore-

casting over the fast few decades such as legacy classical forecasting models

including exponential smoothing, regression models, autoregressive integrated

moving average (ARIMA) models, grey forecasting model (GM), and kalman

ﬁlters [5]. The aforementioned forecasting models forecast the electric load but

the accuracy is not up to the desired level due to their inherent limitations. The

linear regression models depend on historical data and are not suitable to solve

the non-linear problems. The ARIMA models taking into consideration previous

and present data points while ignore other inﬂuencing factors. The GM mod-

els can only solve the problems with exponential growth trends. To overcome

the aforementioned problems, in recent years, more eﬀective models have been

proposed to forecast electric load, such as an artiﬁcial neural network (ANN),

multi-layer perceptron (MLP), radial basis fuzzy logic, machine learning, and

intelligent system [6]. Though these eﬀective methods outperform legacy meth-

ods, however, the provide accuracy is not satisfactory due to their limitations.

The ANN-based models trapped into local minima and expert systems strongly

rely on supervised learning. In this regard, integrated and hybrid models are

developed [7], which are the combination of diﬀerent individual models. The

hybrid models outperform than individual models in terms of forecast accuracy.

In this paper, a novel FCRBM based electric load forecasting (FCRBM-

ELF) model is proposed, which is a hybrid model. The major contributions are

demonstrated as follows:

•The proposed model takes into account the exogenous inﬂuencing parameters

in addition to historical electric load data for accuracy improvement.

•The new concept of candidates interaction is introduced for features selec-

tion. Also, the mutual information (MI) technique based features extraction

criteria are extended to measure the candidate’s interaction in addition to

their relevancy and redundancy process.

•Due to better accuracy and fast convergence, RELU and is used with FCRBM

which none of the existing models have used.

•The proposed GWDO algorithm is used in the optimizer to ﬁne tune the

adjustable parameters for feature selection technique to improve the forecast

accuracy with aﬀordable convergence rate.

The remaining paper is structured as follows: Sect. 2demonstrates related work,

Sect. 3brieﬂy describes the proposed system architecture, in Sect. 4, simulation

results and discussions are described. Finally, Sect.5conclude the paper.

2 State of the Art Work

Electric load forecasting strategies are developed for many years in literature due

to its importance in the decision making of SG. The forecasting strategies are

categorized into four categories according to the forecasting period [8]. The ﬁrst

category is the very short-term forecasting [9] which corresponds to less than one

day. The second category is the short-term forecasting which corresponds to the

An Innovative Model Based on FCRBM for Load . . . 51

forecasting period of one day to one-week [10]. The third category is medium-

term forecasting which corresponds to one week and a year ahead forecasting [11].

The fourth category is the long-term forecasting which corresponds to more than

a year ahead forecasting [12]. Statistical tools and AI-based tools are commonly

used for electric load forecasting. The recent and related work is summarized in

Table 1.

3 The Proposed System Architecture

In literature, many authors used ANN based forecaster for load prediction due

to its capability to predict the nonlinearity of consumers load. However, the per-

formance of ANN-based models is not satisfactory in terms of accuracy. Thus,

some authors integrated optimization module with ANN based forecaster, which

improves signiﬁcantly the forecast accuracy. However, the accuracy is improved

at the cost of slow convergence rate. Moreover, the ANN-based models are suit-

able for small data size while their performance is degraded as the data size

increases. Thus, we proposed a new electric load forecasting model based on

FCRBM as shown in Fig. 1. The proposed model is subjected to accuracy, con-

vergence rate, and scalability. The proposed system architecture comprises of

four modules: (1) data processing and feature selection module, (2) FCRBM

based forecaster module, (3) GWDO based optimizer module, and (4) utiliza-

tion module. The detailed description is as follows:

3.1 Data Processing and Features Selection Module

The input data including historical load data and exogenous data (temperature,

humidity, wind speed, and dew point) is fed into the data processing and features

selection module. At ﬁrst, the data cleansing is performed to recover the missing

and defective values. Then, the clean data is normalized to remove the outliers

and make the data within the limit of the activation function. The input data

(X) includes electric load data (P(h, d)), temperature data (T(h, d)), humidity

data (H(h, d)), dew point (D(h, d)), and wind speed (W(h, d)). The hshows

particular hour and dshows particular day of historical data. The tempera-

ture, humidity, dew point, and wind speed are called exogenous variables. The

normalized data is passed to through irrelevancy ﬁlter, redundancy ﬁlter, and

candidate interaction phase subjected to removal of irrelevant, redundant, and

nonconstructive information. The detailed description of relevancy, redundancy,

and candidates interaction phases of features selection technique are as follows:

Relevancy Operation The relevance of candidates input to the target vari-

ables is signiﬁcant for abstractive features selection. For relevancy measurement

in literature many techniques are used in which MI features selection technique

is good. The MI measures the relevance between two variables xand y.The

MI measurement is interpreted as observing yby on xand vice versa. The

52 G. Hafeez et al.

Table 1. Recent and related work summary

Techniques Objectives Dataset Remarks

ARIMA and exponential

smoothing [9]

Forecast accuracy improvement for

real-time scheduling of power

generation

Great Britain

grid

The accuracy is improved for univariate methods while

the accuracy is low for multivariate methods

ANN and self-organizing

map [13]

Decision support system to

commercialize company bidding

Spanish grid This model used meteorological and load data and

ignored exogenous parameters which have a strong

impact on the forecast accuracy

Diﬀerential polynomial

neural network [14]

To reduce the generation cost and

spinning reserve capacity

Canadian grid This model has less accuracy and slow convergence which

have a direct impact on spinning reserve and cost

ANN, ARIMA, and GM

[15]

Accuracy improvement of the bulk

power system

Fuj i an pr ovi nce

of China

The accuracy is improved by incorporating large

exogenous parameters at the expense of slow convergence

rateandhighcomplexity

Reglet and Elman neural

network [16]

Improvement of the accuracy and

capability for eﬀective power system

operation

AEMC This model have large complexity that directly impacts

the convergence rate

Support vector regression

[17]

Accurate load forecasting to minimize

energy imbalance and its associated

cost

Irish CER The parameters are optimally adjusted by the intelligent

algorithm which improved the forecast accuracy at the

expense of high execution time

ARMAHX and

quasi-newton algorithm

[18]

Forecast accuracy improvement for a

market agent and system operators

Spanish and

German energy

market

The accuracy is improved by incorporating sigmoidal

function, however, the execution time and complexity is

increased

ANN, SVR, and fuzzy

interaction regression [19]

Resilience improvement against data

integrity attacks

GEFC 2012 The resiliency of the power system is improved at the cost

of high modeling complexity

MI, ANN, and mEDE

[21]and[20]

Accuracy and convergence rate

improvement for EKPC and Daytown

grid of USA

PJM market This model is suitable for small data size and their

performance are degraded for large data size

ANN-based hybrid

models [22]and[23]

Accuracy improvement of microgrid PJM market The ANN-based models improved the forecast accuracy

at the cost of high execution time

An Innovative Model Based on FCRBM for Load . . . 53

Fig. 1. The proposed system architecture

MI for continuous variables xand yis deﬁned I(x;y) for both individual

(p(x),andp(y)) and joint probability distribution (p(x, y)). Assume that

S={x1,x

2,x

3,...,x

M},(1)

where Srepresents the set of candidate inputs and yis the target variable.

The relevance of each candidate input with target variable yare checked. The

relevance of candidate input xiwith target variable yis deﬁned by the following

Equation

D(xi)=I(xi;y),(2)

where D(xi) represents candidate inputs to target variables.

Redundancy Operation Many authors modeled the redundancy operation

between the candidate inputs. The purpose is to remove the redundant infor-

mation from the input data to improve convergence rate. The redundancy is

evaluated in terms of the mutual information among the two candidate inputs.

In literature, authors demonstrated that closely related candidate inputs reduce

the performance of feature selection technique. The reason is that two candidate

inputs have a large number of mutual information and less redundant informa-

tion about the target variable. So, a variable with less redundant information

54 G. Hafeez et al.

about the target variable which may be incorrectly count as redundant and

will be discarded, while it may be the key feature for forecaster. To overcome

the aforementioned problem a redundancy measure based on interaction gain is

modiﬁed as:

RM(xi,x

s)=Ig(xi;xs;y)

=I[(xi,x

s); y]−I(xi;xs)−I(xs;y),(3)

where RM(xi,x

s) is the redundancy measure, xi,x

sare candidate inputs, and

yis the target variable. The Ig can be mathematically modeled in terms joint

and individual entropy as:

Ig(xi;xs;y)=H(xi,x

s)+H(xi,y)+H(xs,y)−H(xi)−H(xs)−H(y)−H(xi,x

s,y),

(4)

where H(xi), H(xs), and H(y) denote individual entropy and H(xi,x

s),

H(xi,y), H(xs,y), and H(xi,x

s,y) denote joint entropy.

Interaction Session In [22], used redundancy and irrelevancy ﬁlters for fea-

ture selection. However, the individual features may be irrelevant but become

relevant when used together with other input candidates. Thus, the feature selec-

tion technique can be extended to interaction among the candidate inputs. If two

candidate inputs xiand xshave redundant information about target y, then the

joint MI of both candidates with ywill be less than the sum of individual MIs.

Thus, the result will be negative according to Eq. 3, which indicates redundant

features xiand xsfor the forecaster. The absolute value of Eq.3shows the

amount of redundancy. On the other hand, if xiand xscandidate inputs inter-

act with target ytheir interaction causes joint (xiand xs) MI with target y

greater than the sum of individual MIs. Thus, the positive value of Eq.3indi-

cates interacting features and its absolute value shows the amount of interaction.

Hence, for redundancy and interaction the Eq. 3can be modiﬁed as:

RM(xi,x

s)={Ig(xi;xs;y),if Ig(xi;xs;y)<0

0 otherwise (5)

In(xi,x

s)=Ig(xi;xs;y),if Ig(xi;xs;y)>0

0 otherwise (6)

where Eq. 5is modiﬁed equation for redundancy measure and Eq. 6is for inter-

action measure. Thus, the abstractive features are selected and fed into the

forecaster module based on FCRBM.

3.2 FCRBM Based Forecaster Module

The purpose of this module is to devise a framework which is enabled via learn-

ing to forecast the future electric load. From Sect. 2it is concluded that all

forecast models are capable to predict nonlinear electric load proﬁle. Thus, we

chose FCRBM for forecaster module due to two reasons: (a) it predict the non-

linear electric load with reasonable accuracy and convergence rate, (b) and its

An Innovative Model Based on FCRBM for Load . . . 55

performance is improving with the scalability of data. FCRBM is a deep learning

model. It has four layers i.e., hidden layer, visible layer, style layer, and history

layer. Each layer has a particular number of the neuron. In the forecaster module,

FCRBM is activated by rectiﬁed linear unit (RELU) activation function. The

RELU is chosen among the activation function because it overcomes the prob-

lems of overﬁlling and vanishing gradient, and has fast convergence as compared

to other activation functions. The mathematical model of RELU is mentioned

in Eq. 7.

f(x) = max(0,x)

f(x)1ifx≥0

0 otherwise

(7)

The training and learning procedure iterates for a number of epochs to forecast

the future load. To update weight and biases during training processes authors

used diﬀerent algorithms, i.e., gradient descent and backpropagation, levenberg-

marquardt algorithm [23], and multivariate autoregressive algorithm [21]. The

levenberg-marquardt algorithm trains the network faster as compared to gradient

descent and backpropagation. Thus, the multivariate autoregressive algorithm

is used for network training due to its fast convergence and better performance.

The selected feature of data processing module S1,S

2,S

3,...S

nis fed into the

forecaster module, where the forecaster constructs training and testing data

samples. The ﬁrst three years of data samples are used for network training. On

the other hand, the last year data samples are used for testing. The purpose is

to enabled FCRBM based forecaster module via training to forecast the future

load. The forecaster module returns error signal and the weights and biases are

adjusted as per multivariate autoregressive algorithm. This error signal is fed

into the optimization module to improve the forecast accuracy.

3.3 GWDO Based Optimizer Module

The preceding module returns the future predicted load with some error, which

is minimum as per the capability of FCRBM, RELU, and training algorithm.

To further minimize the forecast error the output of the forecaster module is fed

into the optimizer module. The purpose of the optimizer module is to minimize

the forecast error. Thus, the error minimization becomes an objective function

for the optimizer module and can be mathematically modeled as:

Minimize

Rth ,I

th,C

i

Error (x)∀x∈{h, d}(8)

where Rth is redundancy threshold, Ith is irrelevancy threshold, and Ciis can-

didates interaction. The optimizer module is based on our proposed GWDO

algorithm. The optimizer module optimizes Rth ,Ith ,andCiand feedback these

parameters to data processing module. In data processing module, feature selec-

tion technique use optimized values of Rth ,Ith thresholds and Cicandidates

interaction for optimal selection of features. The integration of optimizer mod-

ule with the forecaster module increase forecast accuracy at the cost of high

56 G. Hafeez et al.

execution time. Usually, the integration of optimizer with the forecaster module

is preferred for those applications where accuracy is of high importance compared

to convergence rate. For optimization, various techniques are available like lin-

ear programming, non-linear programming, convex programming, quadratic pro-

gramming, and heuristic techniques. Linear programming is avoided because the

optimization problem is non-linear. The non-linear programming is applicable

here and returns more accurate results at the cost of large execution time. The

convex optimization and heuristic optimization suﬀers from slow and premature

convergence, respectively. Similarly, the DE [22] and mEDE [21] are not adopted

because of slow convergence, low precision, and trapped into optimum. To cure

the aforementioned problems we proposed GWDO. In other words, GWDO algo-

rithm is preferred because it provides an optimal solution with a fast convergence

rate. The proposed GWDO algorithm is a hybrid of GA and WDO. The GA

enables the diversity of population and WDO has fast convergence. The fore-

casted future load is utilized in the utilization module for planning, operation,

and unit commitment.

3.4 Utilization Module

The forecasted load is utilized for long term planning that needed state permits

ﬁnancing, right of ways, transmission and generation equipment, power lines

(transmission lines and distribution lines), and substation construction.

4 Simulations Results and Discussions

For the performance evaluation of the proposed FCRBM-ELF model simulations

are conducted in Matlab 2016, which is installed on a laptop having speciﬁca-

tions of Intel(R) Corei3-CPU @2.4GHz and 6GB RAM with Windows 10. The

proposed FCRBM-ELF model is compared with existing models i.e., MI-mEDE-

ANN [20], AFC-STLF [21], Bi-level [22], and FS-ANN [23]. The aforementioned

models are chosen due to closer similarity with the proposed model. For testing

the proposed model real time hourly load data of FE grid is used. The dataset

is taken from publicly available pennsylvania jersey maryland (PJM) [25]. The

dataset is also considered in [21]. The dataset is of four years from 2014 to 2017.

The ﬁrst three years of data is used for training the FCRBM and last year data

is for testing. The parameters used in simulations can be justiﬁed in [21]. The

parameters listed are kept constant for existing and proposed model subjected

to a fair comparison. The proposed model is tested in terms of four performance

metrics, i.e., MAPD, RMSD, correlation coeﬃcient (R) and execution time.

The ﬁrst three performance metrics correspond to accuracy, which is deﬁned

as:

•Forecast accuracy: accurcay = 100-Error().

The last performance metric (execution time) corresponds to convergence rate,

which is deﬁned as:

An Innovative Model Based on FCRBM for Load . . . 57

•Convergence rate: execution time, the time required for a forecast model to

complete its execution. The forecast model which have small execution time

converges fast and vice versa. The execution time in this paper is measured

in seconds.

The detailed description as follows:

4.1 Hourly Electric Load Prediction

The evaluation of hourly forecasted electric load of FE grid for the proposed fore-

cast model (FCRBM-ELF) vs existing models (MI-mEDE-ANN, AFC-STLF,

Bi-level, and FS-ANN) is illustrated in Fig. 2. It is clear that the proposed

FCRBM-ELF model eﬀectively forecasts the future load of FE grid. Both ANN

and FCRBM based forecasters are capable to capture the nonlinearities of his-

torical load time series data. The nonlinear prediction capability is due to the

use of nonlinear activation functions (AFs) i.e., sigmoidal, rectiﬁed linear unit

(RELU), and tangent hyperbolic (Tanh). The existing models (MI-mEDE-ANN,

AFC-STLF, Bi-level, and FS-ANN) used sigmoidal AF and our proposed model

select RELU because it has a fast convergence rate and solves the problems of

overﬁtting and vanishing gradient. Figure 2depicts that the proposed FCRBM-

ELF model proﬁle closely follows the target load proﬁle as compared to exist-

ing models (MI-mEDE-ANN, AFC-STLF, Bi-level, and FS-ANN). It is clearly

seen that the percentage error of the proposed FCRBM-ELF model is 1.10%,

MI-mEDE-ANN is 2.2%, AFC-STLF is 2.1%, Bi-level is 2.6%, and FS-ANN is

3.6%, respectively.

0 2 4 6 8 10 12 14 16 18 20 22 24

620

640

660

680

700

720

740

760

780

800

Target

Fig. 2. Hourly load prediction of FE grid

58 G. Hafeez et al.

4.2 Seasonal Electric Load Forecasting: Weekly Prediction with

Hourly Resolution

The weekly electric load forecasting with hourly resolution is depicted in Fig. 3.

This is the week ahead forecasted electric load of FE grid. It is worth mention-

ing that the proposed FCRBM-ELF model has better results as compared to

the existing models (MI-mEDE-ANN, AFC-STLF, Bi-level, and FS-ANN). The

proposed FCRBM-ELF model closely follows the target load which is clearly

depicted in the zoomed box. The observation in terms of numerical values is

that the percentage error of the proposed FCRBM-ELF model is 1.12%, MI-

mEDE-ANN is 2.23%, AFC-STLF is 2.0%, Bi-level is 2.5%, and FS-ANN is

3.4%, respectively. The well-grounded reasons the for better performance of the

proposed FCRBM-ELF model are the use of deep layer layout of FCRBM with

RELU and integration of GWDO based optimization module.

Fig. 3. Seasonal electric load forecasting for a week with an hourly resolution of FE

grid

4.3 Performance Evaluation in Terms of Error and Convergence

Rate

The performance analysis in terms of accuracy (error) and convergence rate (exe-

cution time) is illustrated in Figs. 4and 5. The error indicates how much the

forecasted value deviates from the target value. The smaller value of error results

in high accuracy and vice versa. The error performance in terms of numerical val-

ues for both day and week ahead forecast is shown in Figs.4and 5, respectively.

The percentage error of FCRBM-ELF, MI-mEDE-ANN, AFC-STLF, Bi-level,

and FS-ANN, 1.10, 2.2, 2.23, 2.6, and 3.6%, respectively. From the above dis-

cussion, it is concluded that Bi-level strategy is better than FS-ANN strategy

in terms of error performance. The reason for this better performance is that

An Innovative Model Based on FCRBM for Load . . . 59

forecast error is minimized by the integration of EDE based optimization mod-

ule. However, this percent error is minimized at the cost of more execution time

as depicted in Fig. 5. This Figure shows that the execution increases from 20 to

95 s as the optimization module is integrated. Thus, it is concluded that there

exists a tradeoﬀ between accuracy and convergence rate. The proposed FCRBM-

ELF model reduces this execution time due to the following reasons: (i) GWDO

3is used in the optimization module instead of EDE and mEDE due to faster

convergence, (ii) RELU is used instead of sigmoidal AF and multivariate autore-

gressive algorithm, (iii) FCRBM is used which performs better than ANN, (iv)

for data pre-processing data cleansing and normalization are used, and (v) for

features selection redundancy, irrelevancy, and candidate interaction process are

used, while the existing models only use redundancy and irrelevancy. The afore-

mentioned modiﬁcations in the existing models (MI-mEDE-ANN, AFC-STLF,

and Bi-level) leads to reduce the execution time of 38 seconds. On the other

hand, the proposed FCRBM-ELF model accuracy is improved as compared to

existing models (MI-mEDE-ANN, AFC-STLF, Bi-level, and FS-ANN) [refer to

Fig. 4]. However, the execution time of the proposed FCRBM-ELF model is more

as compared to FS-ANN because with FS-ANN model no optimization module

is used [refer to Fig. 5]. Thus, it is concluded from the above discussion that

the proposed FCRBM-ELF model outperforms the existing models in terms of

convergence rate and accuracy.

Fig. 4. FE grid Electric load forecast: accuracy analysis in terms of percentage error

60 G. Hafeez et al.

Fig. 5. FE grid Electric load forecast: accuracy analysis in terms of Convergence rate

5 Conclusion

In this paper, the electric load forecasting problem is described. This problem is

very complex due to the nonlinear behavior of consumers and inﬂuencing factors.

Thus, an eﬃcient electric load forecasting model based on FCRBM is proposed

to provide accurate load forecast with aﬀordable execution time. The proposed

model is examined on FE grid data of USA. The obtained results are compared

with other load forecasting models (MI-mEDE-ANN, AFC-STLF, Bi-level, and

FS-ANN) in terms of both accuracy and convergence rate. It is validated that

our proposed FCRBM-ELF model outperforms the other models in terms of

forecast accuracy and convergence rate.

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