power factor correction - neural network

8/14/2019 Power Factor Correction - Neural Network

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Power factor correction technique based on artificialneural networks

S. Sagiroglu a, I. Colak b, R. Bayindir b,*

a Department of Computer Engineering, Faculty of Engineering and Architecture, Celal Bayar Bulvari, Gazi University,

Maltepe, Ankara 06570, Turkeyb Department of Electrical Education, Faculty of Technical Education, Gazi University, Besevler, Ankara 06500, Turkey

Received 3 August 2005; accepted 15 February 2006

Available online 29 March 2006

Abstract

This paper presents a novel technique based on artificial neural networks (ANNs) to correct the line power factor withvariable loads. A synchronous motor controlled by the neural compensator was used to handle the reactive power of thesystem. The ANN compensator was trained with the extended delta-bar-delta learning algorithm. The parameters of theANN were then inserted into a PIC 16F877 controller to get a better and faster compensation. The results have shown thatthe proposed novel technique developed in this work overcomes the problems occurring in conventional compensatorsincluding over or under compensation, time delay and step changes of reactive power and provides accurate, low cost

and fast compensation compared to the technique with capacitor groups. 2006 Elsevier Ltd. All rights reserved.

Keywords: Artificial neural network; Power factor correction; Synchronous motor

1. Introduction

In electrical systems, all inductive loads fed by alternating current draw active and reactive powers from theline. While the active power is converted into heat, light and mechanical energy or other types of energy, the

reactive power cannot be converted. It causes the transformer, alternator, cable, protection relay and otherequipment to be larger than their rated values. Therefore, reducing the capacities of production, transmissionand distribution of the line is the result of the effects of lower power factor [1,2]. In order to get rid of thiseffect, the power factor needs to be corrected [3].

In practical applications, reactive power compensations have generally been achieved by employing con-stant capacitor groups using some relays, timers and contactors. These types of systems are known as classicalmethods and have some mechanical problems, slow responses, over or under compensation and harmonics

0196-8904/$ - see front matter 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2006.02.018

* Corresponding author. Tel.: +90 312 212 6820/1221.E-mail address:[email protected](R. Bayindir).

Energy Conversion and Management 47 (2006) 32043215

www.elsevier.com/locate/enconman
mailto:[email protected]:[email protected]


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in the line voltage due to step changes of the capacitor groups that occur during operation. The changes ofreactive power produced by variation of the load or load switching on the line can cause adverse effects onvoltage stability and system security [46]. Nevertheless, static volt-ampere reactive (var) compensators(SVCs) can give smooth reactive power compensation without step changes. SVCs can be classified in fourcategories [712]: thyristor controlled reactor (TCR), thyristor controlled capacitor (TSC), combinations of

TCR and TSC with switched or fixed capacitor and advanced static var compensation (STATCOM). Theseare utilized to enhance the integrated voltage stability. TCRs (or TSCs) for reactive power compensation sys-tems are faster and do not have any mechanical problems. However, they generate harmonics in the voltageand current and cause a stability problem in the system[1318]. These problems can be overcome by using asynchronous motor (SM), if it is already available in the system [19]. Synchronous motors can operate atunity, lagging or leading power factor condition [20,21]. When the motor is operating at unity condition,its power factor is equal to 1.0, and it only draws active power from the line to compensate its mechanicallosses. When it is operating at lagging condition, its power factor is less than 1.0, and it draws lagging reactivepower from the line. When it is operating at leading condition, its power factor is again less than 1.0, but thistime, it produces leading reactive power for the line.

Since the synchronous motor is operating at an over or under compensation condition, the transmissionline can be over loaded by the reactive powers produced or drawn by the synchronous motor. The use of a

synchronous motor as a reactive power compensator is a well known method, but if it is only used for reactivepower compensation, the system will be very inefficient and expensive in comparison with a group of capac-itors[1,5].

Synchronous motor operation is important to reduce the cost and var penalties, to improve the voltage sta-bility of the system, it can be operated by exciting its field circuit either using a fixed DC supply for constantloads or a variable direct current (DC) supply for variable loads. The variable DC supply can be achievedeither manually or automatically. Manual control requires a serial rheostat in the field circuit, which causesa step change of the field current, electrical arcs on the rheostat, over or under compensation and time delayfor the compensation. To get rid of these problems, the field voltage of the SM has to be adjusted using dif-ferent automatic control techniques. Proportional plus integral (PI), proportional plus integral plus derivative(PID), pulse width modulation (PWM) and fuzzy logic (FL) techniques have been used for improving the

compensation [4,22,23]. If one of these automatic controllers is not used in operation, the system might beoperating under the effects of potential pole slip, increasing the kVA loading on the plant transformer andreducing the system voltage. So, using an appropriate controller, the system voltage stability of the bus mightbe achieved or the requirement of the kVA loading for the plant transformer is decreased [5].

Artificial neural networks (ANNs) have been very popular for applying in many engineering fields becauseof their fascinating features, such as learning, generalization, faster computation and ease of implementation.ANNs have been recently applied for power system security, power system stability estimation and optimalSVC and controlling induction, direct current and synchronous motors [2431].

This paper introduces a novel technique based on ANNs to correct the power factor using a dynamic reac-tive power compensator. The experimental data used to design, train and test the neural controller wereachieved from the test rig. Using an ANN compensator totally removes the problems mentioned earlier.Moreover, the exact field current required by the load can be produced without any delay compared to theother methods presented in the literature.

2. Power factor correction

The electrical power produced by an alternator is transmitted, distributed and then used by loads. On apower line, besides the active power, reactive power must also be available for inductive loads. An alternatorin the power station can produce the reactive power for the line, but the reactive power also can be suppliedfrom any source, which can either be a synchronous motor or capacitor groups connected near the load. Thesource of the reactive power must be very close to the load for efficient operation of the system. If the reactivepower of any load is supplied from a synchronous motor or a group of capacitors rather than the power line,this system is called a reactive power compensator [32]. So, the power factor of the system can be kept at a

required value.

S. Sagiroglu et al. / Energy Conversion and Management 47 (2006) 32043215 3205


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The power factor is denoted as pfor cosu. It is the ratio of the active power (P) to the apparent power (S),which can also be calculated fromFig. 1:

pf Active Power

Apparent Power

P

S. 1

The typicalpffor alternating current (AC) electrical machines and any other inductive loads are between 0.35and 0.85. Reactive power for these machines must be available to produce the magnetic field inside the ma-chines for their operation. If the reactive power is compensated somehow, the capacity of the power line isincreased. A commonly used reactive power supply is a group of capacitors. On the other hand, synchronousmotors can operate at leading power factor conditions using a dynamic compensator, and they have been veryreliable for reactive power compensation and do not produce any harmonics in the system[4,33].

The reactive power drawn from the line by an inductive load lags the active power by 90 . If a capacitor isconnected to the system, it also draws reactive power, but it leads the active power. The direction of the capac-itive reactive power (Qcap) is opposite the direction of the inductive reactive power ( Qind) as shown in thegraphical representation of the power factor correction inFig. 1.

The effective inductive reactive power drawn by the circuit will be reduced by the capacitive reactive power,

resulting in a reduction of the apparent power fromStoS1. The phase angle between the active power,P, andthe new apparent power, S1, also is reduced from u to u1. Thus, the power factor increases from cosu tocosu1. So, the new pfis

New pf cos u1 P

S1. 2

By selecting a suitable capacitor value, the power factor can be compensated nearly to 1.0. However, in prac-tice, the power factor is improved to fall between 0.90 and 0.95.

Since the power factors of consumer type loads are very low, the average power factor of the line becomeslower. The power factor of a running loaded or unloaded synchronous motor can be at unity, lagging or lead-ing conditions by changing its excitation current under constant load and terminal voltage. If the excitation

current is reduced while the motor is running at unity condition, the power factor shifts to the lagging con-dition. If the excitation current is increased, and the motor is running at unity condition, the power factorshifts to the leading condition. Furthermore, the excitation current can also change the reactive componentof the apparent power, but the active component stays constant.

For an ideal compensation, the features of low cost, fast computation and more accuracy are desired forbuilding a new compensation system.

P

S1

Qcap

O ld

V A

r(be

fore

pf

co

rre

cti

on

)

NewVAr(afterpfcorrection)

S

Q cap

Qind

90

901

Fig. 1. Reactive power compensation with capacitors.

3206 S. Sagiroglu et al. / Energy Conversion and Management 47 (2006) 32043215


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3. Artificial neural networks

Artificial neural networks (ANNs) are biologically inspired intelligent techniques. ANNs are generallymade of a number of simple and highly interconnected processing elements organized in layers as shown inFig. 2. These processing elements or neurons process information by its dynamic state response to external

inputs. ANNs are capable of learning patterns by being trained with a number of known patterns. The learn-ing process automatically adjusts the weights and thresholds of the processing elements. Once adjusted withminimal differences between the ANN output and the targeted output, the neural network is said to be trained.

Artificial neural networks have many structures and architectures [34,35]. Multi-layered perceptrons(MLPs) are the simplest and, therefore, most commonly used neural network architectures [35].Fig. 2showsan MLP with three layers: an input layer, an output layer and an intermediate or hidden layer. Neurons arerepresented with circles. Neurons in the input layer only act as buffers for distributing the input signals xitoneurons in the hidden layer. Each neuronjin the hidden layer sums up its input signalsxiafter weighting themwith the strengths of the respective connectionswjifrom the input layer and computes its output yjas a func-tion fof the sum:

yj fX

wjixi

; 3

fcan be a sigmoidal or a hyperbolic tangent function. The output of the neurons in the output layer is com-puted similarly. A number of learning algorithms were used to adjust the weights of the ANNs. The extendeddelta-bar-delta (EDBD) learning algorithm used to train the neural architecture is introduced below.

This algorithm is an extension of the delta-bar-delta (DBD) algorithm and is based on decreasing the train-ing time for multi-layered perceptrons. The use of momentum heuristics and avoiding the cause of wild jumps

1yny

1x 2x mx

Output Layer

Hidden Layer

Input Layer

2y

outputs

inputs

Weights

Weights

Fig. 2. A multi-layered perceptron.



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in the weights are the features of the algorithm developed by Minai and Williams [36]. The EDBD algorithmincludes a little used error recovery feature that calculates the global error of the current epoch during training[36]. If the error measured during the current epoch is greater than the error of the previous epoch, then thenetworks weights revert back to the last set of weights that produced the lower error.

In this algorithm, the changes in weights are calculated as

Dwk1 akdk lkDwk 4

wherea(k) andl(k) are the learning and momentum coefficients, respectively. Dw(k) is the previous change ofthe weights and d(k) is the gradient component. The weights are then found as

wk 1 wk Dwk1. 5

The learning coefficient change is given as

Dak

jaexpcajdkj if dk 1dk > 0;

uaak if dk 1dk < 0;

0 otherwise,

8>:

6

where ja is the constant learning coefficient scale factor, exp is the exponential function, ua is the constantlearning coefficient decrement factor and cais the constant learning coefficient exponential factor. The changein momentum coefficient is also written as

Dlk

jl expcljdkj if dk1dk > 0;

ullk if dk1dk < 0;

0 otherwise,

8>:

7

where jl is the constant momentum coefficient scale factor, ul is the constant momentum coefficient decre-ment factor, cl is the constant momentum coefficient exponential factor and dk is the magnitude of theweight gradient component. As can be seen from Eqs.(6) and (7), the changes of the learning and momentum

coefficients have separate constants controlling their increase and decrease.d(k) is used whether an increase ordecrease is appropriate. Therefore, the increases in both of the coefficients were modified to be exponentiallydecreasing functions of the magnitude of the weighted gradient components jdkj. Thus, greater increases willbe applied in areas of small slope or curvature than in areas of high curvature. This is a partial solution to the

jump problem. In order to take a step further to prevent wild jumps and oscillations in the weight space, ceil-ings are placed on the individual connection learning and momentum coefficients. For this, a(k) 6 amax andl(k) 6 lmax must be satisfied for all connections, where amax is the upper bound on the learning coefficient,and lmax is the upper bound on the momentum coefficient[37].

If the error,E(k), is less than the previous minimum error, the weights are saved as the best current values.A recovery tolerance parameter kcontrols this phase. Specifically, if the current error exceeds the minimumprevious error such thatE(k) > Emink, all connection weights revert to the best set of weights stored in mem-

ory. Further, both coefficients are decreased to begin the recovery [37].

4. Design and implementation of ANN controller for compensation

The block diagram of the proposed compensation system used in the design and implementation is given inFig. 3. The block diagram consists of an ANN controller (ANNC), various inductive loads, cosu meter, asynchronous motor and a field circuit of a synchronous motor. The frame in the diagram shown with thedashed line demonstrates the novel controller presented in this work. The input variables of the proposedANNC are the load current (IL), the power factor error (e), the change of excitation current (DIf) and thepower factor of the system (cosusystem). The only output of the ANNC is the excitation current (If). The powerfactor error is calculated as

e cos uref cosusystem. 8



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The excitation current, If(k), of the synchronous motor can be calculated by adding the change of current, DIf,to its previous value, If(k1), as

Ifk Ifk1 DIf. 9

The design process starts with achieving the input and output tuples of the ANNC given inFig. 3. In order toobtain these tuples, IL, e, cosusystem, Ifand DIf, a test rig shown inFig. 4was setup. The input and outputparameters used to establish the ANNC were achieved from this test rig. The test procedures followed are gi-ven below:

(1) The synchronous motor was driven by an auxiliary machine.(2) AC voltage was applied to the stator windings of the synchronous motor.

a. When the speed of the motor was very close to the synchronous speed, DC voltage was applied to thefield winding of the motor and synchronous operation was started.

b. After starting synchronous operation, the auxiliary machine was disconnected from the synchronousmotor.

(3) As the synchronous motor was running, its field current was adjusted to its minimum value by a rheostatconnected in series to the field circuit.a. At this point of the operation, the motor was drawing minimum current from the supply, and its

power factor was at unity.b. Choosing this point as the reference and keeping the load and applied voltage constant, the field cur-

rent was adjusted by a serial rheostat.c. When the field currentIfwas increased, the motor shifted from unity power factor to leading power

factor operation.

Inductive

load

e

+

PIC 16F877

Field circuit of

synchronous motor

A

B

C

0

Artificial Neural

Network Controller

(ANNC)

refcos

systemcos

systemcos

fkI

)1k(fI

LI

fI

fI

cos meter

fI

Fig. 3. Block diagram of the compensation system based on ANNs.



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(4) This test was repeated for several times at different loads.(5) The parameters were then measured and recorded from the test rig.

The levels of the inputs and the output were between 3.0 6 IL 6 6.0, 0.65 6 cosu6 0.95, 0.05 6 e 6 0.35,1.318 6 If6 2.186 and 0.138 6 DIf6 0.946. The ANNC system only requires appropriate parameter settingsof the inputs, the weights, the biases and the outputs. The input and output parameters achieved from the testrig were used to establish the compensation model based on the ANNs. According to the number of inputsand the output, the number of input neurons and output neurons were assigned. The numbers of neuronsfor the hidden layer were also selected after a couple of trainings. A total of 100 patterns were used in trainingand test. Fifty of them were used in training. The remaining 50 patterns were used in test. The training processstarts with applying all the tuples (patterns) in the training set to the network. Training is stopped when thetraining accuracy of the network is deemed satisfactory according to some criterion (for example, when theroot mean square error between I

tf and Iffor all the training set falls below a given threshold) or the maxi-

mum allowable number of epochs is reached. Once the model parameters were obtained from a proper ANNCtrained with the specified accuracy, the neural parameters achieved were then inserted into a PIC 16F877 con-troller for a real time implementation as shown inFig. 3. The microcontroller has only 35 single word instruc-tions. All are single cycle instructions except for the program branches, which are two cycles. This integratedcircuit operates at 20 MHz clock frequency and runs each instruction as fast as 200 ns. Flash program memoryis up to 8K 14 words. Data memory is partitioned into four banks, which contain the general-purpose reg-isters and the special function registers. Bits RP1 and RP0 are the bank select bits. Each bank extends up to7Fh (128 bytes). The prepared program in C++ is 1096 lines total. The program is compiled by a HITECH C

compiler and then transferred into the PIC. The program was reserved for about two banks or 4 Kbytes. Therequired excitation current by a specific load was calculated and applied to the field circuit of the SM veryrapidly with the help of the ANNC inserted into the PIC.

With this neural controller, the voltage overshoots, and over or lower compensations were effectivelyand efficiently reduced to minimum levels. The ANNC system presented in this work only requires appro-priate settings of the parameters: the numbers of inputs and outputs, the number of neurons in thehidden units, the type of activation function, the learning algorithm and the parameters of the learningalgorithms.

Designing a proper controller is crucial for a successful application. The configuration of the ANN utilizedin this study is illustrated in Fig. 5. The neural network is a four layered one. The numbers of nodes in theinput (X), in the first hidden (H1i), in the second hidden (H2j) and the output layers (Y) are 4, 10, 5 and 1,

V

A

V

+

-

M

3 ~

AA

B

C

0

cos

Inductive

Load

LI

fI

LV

Fig. 4. Test rig used in achieving the input and output tuples.



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respectively. The neurons in both the hidden and output layers have biases. Sigmoid functions were selected inthe hidden and output layers. The inputs were scaled between1.0 and +1.0. The output was scaled between0.2 and 0.8.

The artificial neural network controller (ANNC) was trained with the EDBD learning algorithm asexplained earlier. After a proper training, the ANNC parameters, weights, biases activation functions, numberof neurons and the levels of the input and output values were first achieved in an off line process with softwaredeveloped in C++. The ANNC parameters achieved were finally inserted in a PIC 16F877 controller for the

real time application. After this insertion, the test values obtained from the test rig in Fig. 4were also used totest the ANNC compensator. The test results have shown that the ANNC provides satisfactory results for thecorrection. Using these parameters, it is possible to calculate the value of the excitation current required by thepower factor of the system under a specific load. The flowchart of the developed program is given in Fig. 6.The program helps us to achieve IL, DIL, cosuold, cosunew, DIfand If automatically.

When a user enters the current and power factor of the system between the defined limits to increase thepower factor to 0.98, the changes of the system power factor and the excitation current can be achievedand displayed on the menu. In addition, the old and new values of the power factors are also displayed onthe menu as shown inFig. 7. When the program is run, the calculated values of load current, excitation currentand power factor are saved in a file. The values can be used to produce the graphics of controlled power factoras given inFig. 8. If the test is repeated with different loads, the value of the power factor stays constant with

LI

cos

e

fI

Bias

11H

21H

31H

41H

51H

61H

71H

81H

91H

101H

12H

22H

32H

42H

52H

+1

1X

2X

3X

4X

1YfI

Bias+1

Bias+1

Fig. 5. ANNC configuration.



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respect to the variable load currents. So, the novel technique presented in this work provides acceptable andreliable results.

The experimental and ANNC results in training are given inFig. 8. It is clear to say that the neural modelcompensator follows the experimental results very closely. Fifty test samples, which were never applied to theANNC before, were used to test the neural compensator.Fig. 9demonstrates the performance of the ANNC

in correcting the power factors for the samples applied. The corrected power factors have shown that the

Fig. 6. Flow chart of present compensator.



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present ANNC provides satisfactorily good results. Even if different loads were applied to the ANNC, the

power factor was kept nearly constant.

Fig. 7. Screen shot of the program developed.

1.2

1.4

1.6

1.8

2

2.2

1 3 5 7 9 11 13 15 17 19 21 2 3 25 27 29 31 33 35 37 39 41 43 45 47 49

No of ANN Test Examples

FieldCurrent(A)

Experiments

ANNC

Fig. 8. Verification results achieved from ANNC.



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5. Results and conclusions

A novel power compensation system based on an ANNC was successfully presented in this work. Theresults achieved from this work have shown that the compensation system based on an ANNC performedwell. As mentioned earlier, the features such as low cost, accuracy and fast computation of a compensatorsystem are always required. The proposed ANNC achieves the compensation with these features. Using anANNC for the power factor correction problem provides effective, efficient, reliable and robust results as seeninFig. 9. Inserting the ANNC parameters into the PIC enables low cost and faster computation for the com-pensation. The approximate computation time achieved was about one microsecond. Line stability and max-imum power transfer can be achieved effectively with the proposed compensation scheme.

When the synchronous motor is controlled with an ANN controller, the system becomes very robust andeffective. As a result, there have been no over or lower compensations as demonstrated in Fig. 9. In addition,the problems of classical methods, such as the mechanical problems, harmonics in the voltage waveform, timedelays, step change of excitation voltage, pole slip, kVA loading on the plant transformer, var penalties andvoltage drop on the line, have all been removed, improving the voltage stability, accuracy and effectiveness ofthe system. So, the novel technique presented in this work can be very attractive for industrial applications,since the synchronous motor is available in the system for any other purposes. The proposed system can alsobe used as a voltage regulator for variable loads.

The disadvantages that come across during this work are the requirement of a synchronous motor for reac-tive power compensation, selecting appropriate ANNC parameters, training the ANNC in an off line processand then inserting them into the microcontroller system, which indicates the need of much more work.

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