Real-time Forecasting of Electrical Power System Loads using Moving

Average-Extreme Learning Machine (MA-ELM) Algorithm

VENKATASIVANAGARAJU S.1, M.VENKATESWARA RAO2

1Department of EEE, JNT University Anantapur, Ananthapuramu, A.P, INDIA

2Department of EEE, JNTUACEK, JNT University Anantapur, A.P, INDIA

Abstract: - Load Forecasts are the primary factors which considered by electricity utility companies while

planning power generation, power infrastructural development and load flows etc. Different forecasting

techniques have been proposed from statistical to artificial intelligence-based models and the area of research is

still growing. In our research work, considering the real time data of 33KV bus system which is having 34

buses and 54 lines. In this case, forecast the day ahead scheduling of various parameters such as load real

power (Pload), voltage magnitude at each bus, apparent power flow between buses and total transmission losses

for hourly basis and also forecasted the mentioned parameters for 5 days. The actual real time values are

compared with forecasted values using two existing methods namely Extreme Learning Machine (ELM),

moving average and proposed Moving Average–Extreme Learning Machine (MA-ELM) algorithm. In addition

to this, forecasted the loads and losses for short term and long-term forecasting cases and verified through

MATLAB programming.

Key-Words: - Short term load forecasting (STLF), Moving average (MA), Moving Average-Extreme Learning

Machine (MA-ELM).

Received: May 26, 2021. Revised: March 15, 2022. Accepted: April 13, 2022. Published: May 12, 2022.

1 Introduction

categories, which are very short term, Short-term

and Long-term forecasts. Particularly in power

market these are very significant for the power

system safety. To meet the high demand of urban

electricity, exact and persistent short-term load

forecasting in power systems operation and

management plays an important role, especially in

expansion of generating power, economic load

scheduling and dispatch, and sustainability of

electricity supply. For managing the power systems

utilities [1] in planning, evaluations of market

demand, load switching, reducing cost and finally

guaranteed continuous electricity providing [2]

short-term load forecasting (STLF) is considered as

a key aspect.

Based on diﬀerent parameters it can predict the

future electrical load with the help of electricity load

forecasting. The parameters can be atmospheric

conditions, geographical conditions, economic

conditions, time horizon such as hour, day and

month etc. For the development of smart grid,

predict loads in advance [3] for hourly, weekly or

monthly by the use of Short-term electricity load

forecasting (STLF). To deal with generation of

energy and consumption, forecasting models’

accuracy is very crucible. For the deregulated power

system accurate forecasting model is a very

important aspect. In the literature many works were

done based on forecasting of load. Neural networks,

Time series forecasting technique and a Kalman

ﬁltering estimator are popularly used techniques for

forecasting of load in smart grid applications [4–5].

Auto regressive moving average (ARMA) based

models [6], Kalman ﬁlter [7], exponential

smoothing (ES) [8], linear regression [9], and grey

models (GMs) are called as Statistical models and

are widely used in urban smart grid systems for

short-term load forecasting. Auto regressive

integrated moving average (ARIMA) models are

also used to manage the time series analysis in

Smart grid for short term load forecasting[12].

Based on artiﬁcial intelligence/machine learning

(ML) or conventional methods Load forecasting can

be performed. Based on support vector machines,

fuzzy logic, and artiﬁcial neural networks (ANNs)

[10] methods can give better performance than the

conventional methods. Deep learning for STLF [11]

can be used for further extensions. Because of good

performance and simple implementation ANN

based forecasting method can be preferred among

the ML forecast models.

The objective of the paper is to enrich the accuracy

of forecasting by extreme learning machine

algorithm. In this paper, MA-ELM is a novel hybrid

algorithm has been proposed for forecasting of load

real power, voltage magnitude and transmission line

losses. It has a combinational feature of both

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Venkatasivanagaraju S., M. Venkateswara Rao

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Moving Average and Extreme Learning Machine

(MA-ELM) algorithm. In the present paper, it has

proposed very short term, short term and long-term

forecasting and estimate various parameters such as

load real power (Pload), voltage magnitude at each

bus, apparent power flow between buses and total

transmission losses. From the obtained results,

observed that the MA-ELM algorithm offers good

performance in the point of error metrics and

convergence time rather than Moving Average and

ELM algorithms. In real time, this technique is very

much helpful for forecasting of load[13]. The

forecasting results are obtained through MATLAB

2016a software.

Paper is organized that Section I gives the electric

load forecasting introduction. Section II presents the

mathematical modelling of extreme learning

machine algorithm and moving average approach.

section III describes the proposed methodology and

the proposed model performance through MATLAB

programming is discussed in Section IV.

Fig. 1: Process flow of conversion between STLF

and LTLF.

STLF is the most popular approach among the

various options. Because of its inherent

connectedness to other types of projections, it plays

a crucial role in the creation of economic and secure

operating strategies for the power system. By adding

econometric variables to the STLF and projecting

the model to a longer horizon, the STLF can be

turned into MTLF and LTLF. The VSTLF model,

on the other hand, can be created from STLF by

include the loads from the previous hours as part of

the STLF model's inputs. Short-term load

forecasting can incorporate the autocorrelation of

the current hour load and the preceding hour load.

Additionally, the residuals of previous load can be

gathered and used to create a new series based on

the STLF. By projecting future residuals and adding

them back to the short-term prediction, a very short-

term forecast can be obtained. Figure 1 depicts the

conversion process between STLF and LTLF,

MTLF and VSTLF.

2 Methodology

2.1 Extreme Learning Machine Algorithm

The Extreme Learning Machine model is a Single

Layer Feed-forward Network (SLFN) contains

input, hidden and output layers. Input layer nodes

are interconnected with the hidden layer nodes. This

interconnection is known as input layer weights.

The hidden layer is the layer between the input and

output layers. Each hidden layer nodes are also

interconnected with all the output layer nodes. This

interconnection is known as the output layer

weights. Using different training algorithm weights

can be adjusted. The output nodes has been

represented the horizon of forecast.

The Extreme Learning Machine (ELM) is a new

training algorithm and to reach global minima, it

does not require iterative tuning. When compares to

gradient descent-based training algorithm, this

algorithm has to reduce the training time. The ELM

training speed is very faster while comparing with

gradient-descent based training algorithm. It can

avoid to choose additional parameters like learning

rate and stopping criterion. The empirical evidence

shows that it has universal approximation

capabilities and good generalization.

In ELM, randomly chosen the input weights and

hidden biases (linking the input layer with the

hidden layer), and by using Moore-Penrose inverse

the output weights are determined analytically

(linking the hidden layer with the output layer).

With a smaller number of iterations, the

convergence of ELM is much faster. The ELM can

be modelled mathematically as follows:

Given training set Input and Actual Output

samples, (xi,yi); i=1,2,…….,S, xi ∊ Rp, yi ∊ Rq,

where x and y are the input and target matrices of

dimensions p and q.

With N hidden layer neurons, the SLFN neural

Network is written as

∑𝛽

𝑁

𝑖=1 i.Gi(xj)= ∑𝛽

N

i=1 i.G(wi.xj+bi)=oj (1)

where wi is the hidden layer input weight

matrix, βi is the hidden layer output weight matrix,

bi is the threshold of the hidden layer, and G(x) is

the activation function. To minimize training error

by ELM search:

∑𝛽

N

i=1 i.G(wi.xj+bi) = yj (2)

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The above equations can be re-written as:

Hβ = Y (3)

H is the hidden layer output matrix;

The output weight matrix can be calculated by:

β = H+Y (4)

Where H+ is the Moore–Penrose inverse of H.

2.1.1 Moving Average Approach

In this method, Moving Average formula has been

used to average the mentioned number of periods to

calculate the next forecasted parameter.

3 Proposed MA-ELM Algorithm

For forecasting of future demand of Chittoor

District, APSPDCL, Andhra Pradesh in India, the

proposed MA-ELM algorithm is applied.

Moving Average-Extreme Learning Machine

algorithm:

MA-ELM is a hybrid approach gives combined

features of both Moving average and Extreme

Learning Machine algorithm. Simple Moving

Average approach for prediction and capability of

ELM improves overall efficiency and reduces

simulation time with least training. Moving average

method is purely statistical method, here we have to

possibility to apply error analysis and stability

analysis cannot be applied. The mathematical

formulation of MA-ELM can be explained as

follows:

Let the training set Input and Actual Output sample

patterns be (ai,bi); i=1,2,…….,S,S+1. Where

ai=[ai1,ai2,ai3……., ais, ai(S+1)]T represents input

parameters and bi=[bi1,bi2,……,bis]T represents

output parameters.

Fig. 2: Single hidden layer MA-ELM structure

Where bi1=average of ai1 and ai2, bi2=average of

ai2 and ai3. Similarly, bis=average of ais and ai(s+1).

Mathematical function establishes MA-ELM with

activation function φ(.) and L number of hidden

nodes, it can be expressed as

G(aj)= ∑Ƞ

N

i=1 i.φ(λi.aj+µi);j=1,2,…..(s+1) (5)

The above expression written in matrix notation

as φȠ=Aꚛ (6)

The activation function is φ(.) in matrix form is

Aꚛ is the target matrix,

Aꚛ=[b1,b2,……,bs]T (7)

The parameters λ and µ has been randomly chosen

and cost function is minimised based on back

propagation learning algorithm. The output weight

matrix ῆ can be obtained with the help of singular

value decomposition (SVD) method using Moore–

Penrose inverse approach. It can be calculated as:

ῆ=φ-IAꚛ (8)

In the present work, forecasting of various

parameters has been done for Chittoor District,

APSPDCL area of the state of Andhra Pradesh,

India.

Step 1: Collected the bus data, line data and

previous load data for past ten years belongs to

Chittoor district from APSPDCL Head Office,

Tirupati.

Step 2: Using MA-ELM algorithm forecasting has

been done for selected parameters in the given area.

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Table 1. Pload 4 Results and Analysis

In the present work, considered very short-term load

forecasting and estimate the day ahead scheduling

of various parameters such as load real power

(Pload), voltage magnitude at each bus, apparent

power flow between buses and total transmission

losses for hourly basis and also forecasted the

mentioned parameters for 5 days.

In “Table 1” shown the actual load values,

forecasted loads using ELM, MA method and

proposed MA-ELM method values of load real

power (Pload) for 34 buses. From the tabulated

results, concludes that the proposed method gives

better performance when comparing with the two

existing methods. The results of load real power

with proposed method is shown in “Figure 3”.

Fig. 3: Load real Power Pload

In table.2, shown the actual voltage magnitude

values, forecasted values with ELM, MA methods

and proposed MA-ELM method for 34 buses. The

graphical representation of voltage magnitudes at

buses with proposed and existing methods is shown

in “Fig. 4”. From this, it has observed that by the

proposed method the voltage magnitude is slightly

increased

In “Table 3” mentioned the actual values of

apparent power flows (Sflow) between buses (for 54

lines), forecasted power flows using existing

methods and proposed method values of line flows.

The results of apparent power flows with proposed

method is shown in “Fig 5”. From the output values

understand that the magnitudes of power flows are

optimally scheduled with proposed method.

0

100

200

300

400

1 4 7 10 13 16 19 22 25 28 31 34

Power (MW)

Bus Numbers

Bus No ELM MA MA-ELM Actual load

Bus No

ELM

MA

MA-ELM

Actual load

1

0

2

3

2.96106

2.944104

2.93832

3

41

41.08519

40.97365

41.00963

4

0

5

13

13.02926

12.94748

12.96294

6

75

74.96796

74.94492

74.94274

7

0

8

150

149.979

149.9498

149.9547

9

121

121.0702

120.9629

120.9917

10

5

5.062028

4.957805

4.98477

11

0

12

377

377.0755

376.9617

376.9963

13

18

18.08279

17.96876

18.00453

14

10.5

10.53167

10.45144

10.4661

15

22

21.9578

21.94083

21.93269

16

43

42.9532

42.94533

42.93931

17

42

42.10348

41.97738

42.01925

18

27.2

27.26037

27.1577

27.18444

19

33

33.05279

32.9548

32.97876

20

23

23.0451

22.95806

22.97677

21

0

22

0

23

63

63.09944

62.97272

63.01789

24

0

25

63

62.98244

62.95338

62.95467

26

0

27

93

92.94735

92.94116

92.93127

28

46

46.09253

45.98746

46.02777

29

17

17.09103

16.97226

17.00927

30

36

36.08836

35.97305

36.00931

31

5.8

5.891067

5.770532

5.809697

32

16

16.07071

15.96261

15.99269

33

38

37.98484

37.95064

37.95561

34

0

Total

1381.5

1382.465

1380.48

1380.991

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Fig. 4 Bus voltages

Table 2. Voltage magnitudes at buses

0

0,5

1

1,5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Voltage(Pu)

Bus Number

ELM MA MA-ELM Actual

Bus No

ELM

MA

MA-ELM

Actual

1

177.8435

178.2019

177.4211

177.6142

2

164.0192

164.3714

163.6927

163.8699

3

109.9472

110.1649

109.7072

109.8195

4

25.96752

26.00539

25.90843

25.93136

5

32.50065

32.54326

32.43836

32.46451

6

20.87292

20.89087

20.84959

20.85895

7

42.20619

42.19622

42.19967

42.19535

8

161.5927

161.5807

161.6705

161.6519

9

13.9734

13.98843

13.97114

13.97632

10

19.80122

19.79508

19.81789

19.81347

11

16.07777

16.15178

16.01028

16.04677

12

6.728811

6.767126

6.689216

6.709259

13

40.91338

40.99192

40.84401

40.8835

14

67.91005

68.05626

67.79406

67.8665

15

248.5747

249.0657

248.0789

248.3331

16

110.8514

111.039

110.6442

110.7455

17

125.104

125.3721

124.8971

125.0273

18

55.10505

55.15557

55.04674

55.07441

19

67.83606

68.01067

67.69476

67.77232

20

19.1667

19.18657

19.14373

19.15567

21

98.03861

98.07942

98.01945

98.0366

22

45.70516

45.87023

45.56174

45.64094

23

36.56608

36.62135

36.5173

36.54608

24

57.25011

57.55941

56.96963

57.12219

25

65.61201

65.84177

65.46171

65.56699

26

80.09802

80.25505

79.91992

80.00454

27

91.9482

92.10797

91.80827

91.88828

28

34.46314

34.54896

34.38838

34.42649

29

8.891935

8.912713

8.874242

8.884053

30

44.06563

44.20001

43.94607

44.00537

31

23.00165

23.01186

22.99684

23.00509

32

11.03039

11.02431

11.01211

11.01165

33

28.16451

28.19558

28.14867

28.16312

34

12.3143

12.3157

12.31517

12.31569

35

34.2143

34.24215

34.20262

34.21513

36

47.70539

47.73062

47.65924

47.67647

37

51.54098

51.46888

51.52435

51.49996

38

67.50628

67.51109

67.51172

67.51449

39

98.86686

98.96312

98.83543

98.87702

40

48.06732

48.2026

48.0149

48.07316

41

6.870753

6.909296

6.850406

6.868304

42

1.691388

1.709101

1.691189

1.697704

43

38.71578

38.70075

38.66417

38.66962

44

13.81919

13.8473

13.79286

13.80765

45

13.81919

13.8473

13.79286

13.80765

46

32.74262

32.75351

32.70465

32.71685

47

5.348144

5.359592

5.339327

5.344595

44

13.81919

13.8473

13.79286

13.80765

45

13.81919

13.8473

13.79286

13.80765

46

32.74262

32.75351

32.70465

32.71685

47

5.348144

5.359592

5.339327

5.344595

48

99.8915

100.0664

99.74588

99.83389

49

76.60924

76.67557

76.54085

76.57724

50

53.68711

53.79858

53.58921

53.64279

51

50.64456

50.7404

50.55892

50.60767

52

48.19963

48.28682

48.11582

48.16222

53

45.02944

45.09858

44.98186

45.01595

54

26.96045

26.96407

26.96151

26.96305

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Table 4. Total Power Losses

Fig. 5: Apparent Power Flow

In “Table 4” shown the actual total power losses and

forecasted losses occurred with existing methods

and proposed method. The graphical representation

of total power losses with proposed method and

existing methods are shown in “Fig. 6”. From the

obtained data the total power losses are minimized

with the proposed method when compares with the

existing methods.

In “Table 5” tabulated the actual total power losses

and occurrence of forecasted losses with existing

methods and proposed method for hour wise upto 24

hours on 01-01-2020. “Figure 8” shows the

graphical representation of the power losses on 01-

01-2020. Hence, it has observed that the losses are

minimized with the efficiency of proposed method.

0

50

100

150

200

250

300

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53

Power(MW)

Bus Number

Bus No ELM MA MA-ELM Actual

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Fig. 6: Total Power losses

Table 5. Total Power losses on 01-01-2020

0

10

20

30

40

50

60

70

80

ELM MA MA-ELM Actual

Power(MW)

Method

Total power losses, MW Iterations Time, Sec

Time

Total power losses, MW

Existing methods

MA-ELM

Actual

ELM

MA