transfer capability computations using radial basis function neural network under deregulated power...

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Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (3): 473-481 (ISSN: 2141-7016)

473

Transfer Capability Computations Using Radial Basis FunctionNeural Network under Deregulated Power System

1K.Suneeta,

2J.Amarnath,

2S.Kamakshaiah

1C.V.S.R College of Engineering, Hyderabad, India2J.N.T.U.H College of Engineering, Kukatpally, Hyderabad-85, India

Corresponding Author: K.Suneeta

___________________________________________________________________________AbstractThe main aim of this paper is to determine to analyze the electrical transfer capability among different

electricity markets using repeated power flow technique. Instead of minimizing the total cost in the conventional

problem, in the paper, the transfer capability between two markets or two electricity supply and generation

areas is maximized. To reduce the time required to compute transfer capabilities and also in order to take

advantages of the superior speed of artificial neural network (A) over conventional methods, the radial basis

function network (RBF)-based approach also has been proposed in this paper. Artificial neural networks have

been able to capture this nonlinearity and give good approximation of the relationship. For complete analysis,

transfer capability is computed using the proposed algorithms of repeated power flow module under various

operational conditions. This data is then used to train artificial neural networks to provide real term evaluationon transfer capability of that particular power system. The effectiveness of the proposed methods is investigated

on a three area IEEE 30 bus system with a comprehensive set of operational limits and controls.

__________________________________________________________________________________________

Keywords: deregulation, transfer capability, repeated power flow (RPF), radial basis neural network(RBFN).

__________________________________________________________________________________________

ITRODUCTIOElectric utilities around the world are confronted with

restructuring, deregulation and privatization. In the

environment of open transmission access [William et

al, Abdel et al 2001], transmission networks tend to

be more heavily loaded and transmission service

becomes one of the most critical elements. Power

system transfer capability indicates how much inter

area power transfers can be increased withoutcompromising system security [Ian Dobson et al

2001]. For both planning and operation of the bulk

power market, accurately identifying this capability

provides vital information. It is important for

planners to know the system bottlenecks and i t is also

important for system operators not to implement

transfers which exceed the calculated transfer

capability. Estimates of transfer capabilities must be

updated regularly as to avoid the combined effect of

power transfers from causing an undue risk of system

overloads, equipment damage, or blackouts.

However, being overly conservative over the

estimates of transfer capability will unnecessarily

limit the power transfers and would prove to becostly and an inefficient use of the network.

Due to deregulation, power transfers are increasing

both in amount and in variety. However, this is

necessary as the market for electric power becomes

more competitive. Improving accuracy and

effectiveness of transfer capability computations for

all areas of power systems would prove a very strong

economic incentive. There are a number of methods

and algorithms [Yan Ou et al 2002, Ejebe et al 1998]

for computing total transfer capability (TTC). The

repeated power flow (RPF) method is used in this

work to calculate the transfer capabilities between

different areas of the power system.

The conditions on the interconnected network

continuously vary in real time [Sauer et al 1997].Therefore, the transfer capability of the network will

also vary from one instant to the next. For this

reason, transfer capability calculations may need to

be updated periodically for application in the

operation of the network. In addition, depending on

actual network conditions, transfer capabilities can

often be higher or lower than those determined in the

off-line studies. As these are playing an important

role in both planning and operation of the bulk power

market [Ian Dobson et al 2001], there is a much need

for fast and accurate calculation of the transfer

capabilities. However, as the time taken by these

traditional optimization methods are quite significant,

these methods may not be suitable for onlineapplication. To reduce the time required to computetransfer capabilities and also in order to take

advantage of the superior speed of artificial neural

network (ANN) over conventional methods, the

radial basis function network (RBFN) based

approach also has been developed in this work.

Based on the proposed RPF formulation for

calculating power transfer capability and the strong

generalizing ability of the artificial neural network,

Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (3): 473-481

Scholarlink Research Institute Journals, 2011 (ISSN: 2141-7016)

jeteas.scholarlinkresearch.org


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under which TTC is calculated may also need to be

modified.

Critical Contingencies

During transfer capability studies, many generation

and transmission system contingencies throughout

the network are evaluated to determine which facility

outages are most restrictive to the transfer beinganalyzed. The types of contingencies evaluated areconsistent with individual system, power pool, sub-

regional, and Regional planning criteria or guides.

The evaluation process should include a variety of

system operating conditions because as those

conditions vary, the most critical system

contingencies and their resulting limiting system

elements could also vary.

System Limits

As discussed earlier, the transfer capability of the

transmission network may be limited by the physical

and electrical characteristics of the systems includingthermal, voltage, and stability considerations. Once

the critical contingencies are identified, their impact

on the network must be evaluated to determine the

most restrictive of those limitations. Therefore, the

TTC becomes:

TTC = Minimum of {Thermal Limit, Voltage Limit,

Stability Limit}

As system operating conditions vary, the most

restrictive limit on TTC may move from one facility

or system limit to another.

R Receiving area; S Sending area;

E External area transfer path

Fig.1 A simple interconnected power system

PROBLEM FORMULATIOSReferring to Fig.1, a simple interconnected power

system can be divided into three kinds of areas:

receiving area, sending areas and external areas.Area can be defined in an arbitrary fashion. It may

be an individual electric system, power pool, control

area, sub-regions, etc which consist of a set of buses.

The transfer between two areas is the sum of the real

powers flowing on all the lines which directly

connect one area to the other area. A base case

transfer (existing transmission commitments) is

determined. The transfer is then gradually increased

starting at the base case transfer until the first security

violation is encountered. The real power transfer at

the first security violation is the total transfer

capability.

The objective is to determine the maximum real

power transfers from sending areas to receiving area

through the transfer path. During a transfer capabilitycalculation, many assumptions [Shaaban et al 2000]may arise that would affect the outcome. The main

assumptions used in this study are as follows:

The base case power flow of the system isfeasible and corresponds to a stable operating

point.

The load and generation patterns vary veryslowly so that the system transient stability is

not jeopardized.

The system has sufficient damping to keepwithin steady state stability limit.

Bus voltage limits are reached before thesystem reaches the nose point and loses voltage

stability.

Therefore, at this stage only the thermal limits and

voltage limits will be taken into consideration

together with generator active and reactive power

limits. The power flow solution is the most common

and important tool in power system analysis, which is

also known as the Load Flow solution. It is used

for planning and controlling a system when system is

assumed to be in balanced condition and single-phase

analysis. It determines the voltage magnitudes and

phase angle of voltages at each bus and active and

reactive power flow in each line. The four quantities

associated with each bus are voltage magnitude,

voltage phase angle, real power injection and reactive

power injection.

The Newton-Raphson equations are cast in natural

power system form solving for voltage magnitude

and angle, given real and reactive power injections

and it is used in the calculation of transfer capability

[Wood et al 1996,Rao et al 1996]. The mathematical

formulation can be expressed as follows [Yan Ou et

al 2002]:

Subject to Power Flow Equations:

)(cos||||1

jiijijj

n

j

ii YVVP +==

(1)

)(sin||||1

jiijijj

n

j

ii YVVQ += =

(2)

And Operational constraints

maxmin ggg PPP (3)

maxmin ggg QQQ (4)

maxijij SS (5)

S S

S R

EE


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maxmin iii VVV (6)The objective function to be optimize

=RkRm

kmr PP,

(7)

The control variables in the above formulation are

generator real and reactive power outputs, generatorvoltage settings, phase shifter angles, transformer

taps and switching capacitors or reactors. The

dependent variables in the formulation are slack bus

(swing bus) active and reactive power injections,

regulated bus (generator bus) reactive power

injection and voltage angle.

Equality and Inequality ConstraintsThe equality constraints in the problem formulation

reflect the physics of the power system as well as the

desired voltage set points throughout the system. The

physics of the power system are enforced through the

power flow equations which require that the net

injection of real and reactive power at each bus sumto zero.

The inequality constraints reflect the limits on

physical devices in the power system as well as the

limits created to ensure system security. Physical

devices that require enforcement of limits include

generators, tap changing Transformers, and phase

shifting transformers. This section will lay out the

necessary inequality constraints needed for the

proposed repeated power flow, implemented in this

thesis. Generators have maximum and minimum

output powers and reactive power which add

inequality constraints.

maxmin

maxmin

ggg

ggg

QQQ

PPP

For the maintenance of system security, power

systems have transmission line as well as transformer

MVA ratings. These ratings may come from thermal

rating (current ratings) of conductors, or they may be

set to a level due to system stability concerns. The

determination of these MVA ratings will not be of

concern in this work. It is assumed that they are

given. Regardless, these MVA ratings will result in

another inequality constraint.

maxijij

SS To maintain the quality of electrical service and

system security, bus voltages usually have maximum

and minimum magnitudes. These limits again require

the addition of inequality constraints.

maxmin iii VVV All the equality and inequality constraints considered

in this work are given in the above problem

formulation.

METHODOLOGYIn this work, it is proposed to utilize the repeated

power flow (RPF) method [Yan Ou et al 2002] for

the calculation of transfer capabilities due to the ease

of implementation. This method involves the

solution of a base case, which is the initial system

conditions, and then increasing the transfer. Aftereach increase, another load flow is solved and thesecurity constraints tested. The computational

procedure of this approach is as follows:

i. Establish and solve for a base case

ii. Select a t transfer case

iii. Solve for the transfer case

iv. Increase step size if transfer is successful

v. Decrease step size if transfer is unsuccessful

vi. Repeat the procedure until minimum step size

reached

The flow chart of the proposed method for the

calculation of transfer capability is given in Fig. 2. Toexplain this properly, a few terms need to be

clarified.

Firstly, look at the term, base case. This refers to the

original system configuration before any transfers

have been considered. In this stage, assumptions are

made about the system which will impact on the final

answer. In the base case, the system operating

conditions must be within safe limits, otherwise there

will be no available transfer capability for the system.

To specify the base case, data is given regarding the

generator status, line flow limits and bus voltage

limits.

The term transfer refers to the actual changing of

generator outputs from the base case. For the case of

this thesis, the following convention is used. A

transfer of x MW from generator at bus A to

generator at B is given by decreasing the generator

real power output at bus A and increasing the

generator real power output at bus B by x MW. With

this convention is the assumption that the slack bus

will pick up any losses that may occur due to the new

state of system. Therefore, to solve for the transfer

requires the performing of a transfer as described

above and then solving a power flow for the given

configuration.

The next step is to perform the power flow simulation

and check it against the given security constraints.These constraints can take on many forms. They

might be line flow power limits, bus voltage

magnitude and angle limits or generator capacity

limits. As well as these, a minimum step size is also

required. The step size is the difference between the

previous transfer and the current transfer. It starts off

at a set size, and the transfer is increased by this


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amount until the power flow simulation results in the

breaking of a constraint.

Once a constraint has been reached, the step size is

reduced and thus the transfer is reduced as well. A

new load flow is calculated and the security

constraints are again checked. This continues until

the step size reaches the preset minimum step size. At

this stage, the amount of power which was

transferred at the last successful load flow is the

transfer capacity of the given buses. The final

constraint to be broken is called the binding limit of

the system

To incorporate power system areas into this equation

requires the modification of all generator real poweroutputs within the specified areas. For example, a

transfer from area A to area B requires the reductionof all generator real power outputs from area A and

the increase of all generator real power outputs for

area B. The proposed method of this work has been

examined on a three area 30-bus system.

Ann Based Transfer Capability Calculation

The RBFN is a special class of multi layer feed

forward networks, and the construction of a radial

basis function network (RBFN) is shown in Fig.5.5.

The RBFN model in its most basic form consists of

three layers: the input layer, hidden layer and output

layer [Simon Haykin et al 1999]. The nodes within

each layer are fully connected to the previous layer.

The input variables are assigned to each node in the

input layer and are passed directly to the hidden layer

without weights. The hidden nodes (units) contain theradial basis functions, and are analogous to thesigmoid function commonly used in the BPFN. The

output layer supplies the response of the network to

the activation patterns applied to the input layer. The

transformation from the input space to the hidden

unit space is non-linear, where as the transformation

from the hidden unit space to the output space is

linear. During training, all of the input variables are

fed to hidden layer directly without any weight and

only the weights between hidden and output layers

have to be modified using error signal. Thus, it

requires less training time in comparison to BPFN

model.

The RBFN finds the design of neural network as a

curve-fitting (approximation) problem in a high-

dimensional space that provides the best fit to the

training data. The hidden units provide a set of

functions that constitute an arbitrary basis for the

input patterns when they are expanded into the

hidden-unit space. These functions are called radial

basis functions. The structural model of RBFN is

shown in Fig.3 the hidden layer is comprised of

Gaussian interpolating functions while the output

layer is linear. It is based on a radial decomposition

of the input space [Yan Ou et al 2002]. The spread

constant for the hidden neurons was set to 0.115. The

number of neurons in the hidden layer was

progressively increased one step at a time by using a

constructive algorithm that automatically chooses the

appropriate center of the radial-basis functions. The

maximum number of hidden neurons was set as a

design parameter (from 25 to 100). Although the

classical RBFN scheme produces good results, the

choice of number of hidden units, the number of

input sets and the parameters of the network are

varied by trial and error.

Fig. 3 Architecture of Radial Basis Function Network

w

Step increase variable

Check iflimits areViolated

No

Yes

Select transfer case and

Variable to bechanged

Step back and increase

Variable with smaller steps

Check if

Limits

are

Violated

Yes

Transfer capability

End

No

Fig.2 Flow chart for calculation of transfer capability

.

w

w

w

Input

LayerHidden layer of Output


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478

For RBFN, there are three different learning

algorithms depending on how the centers of the basis

functions are specified [Jain et al 2003,Reface et al

1999]. In the first method, the samples in the training

set are selected as the centers. The linear weights in

the output layers are calculated by minimizing the

error between the targets and actual outputs of the

network. The second training algorithm estimatesappropriate locations for the centers of the radialbasis functions in the hidden layer using K-means

clustering algorithm, then completes the design of the

network by estimating the linear weights of the

output layer. The third algorithm is an error-

correction learning process. To minimize the error

between the targets and the actual responses, the

linear weights and positions of centers and the width

of the units are adapted using a gradient-descent

procedure.

The sequence of the major steps of gradient learning

algorithm for RBFN is as follows.1) Weight Initialization

2) Weights in the output layer are initialized to small

random values.

3) Weights in the hidden layer are determined by the

K-means clustering algorithm.

It provides a simple mechanism for minimizing the

sum of squared errors with k clusters, with each

cluster consisting of a set of N samples x1, x2,

.,xN that are similar to each other. The algorithm

proceeds as follows:

1) A set of clusters {y1, y2,,yk } are arbitrarilychosen.

2) Assign the N samples to k clusters using the

minimum Euclidean distance rule:

X belongs to cluster l if

jl YXYX


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Generation of Training Patterns

The accuracy of the neural network model depends

on the data presented to it during training. A good

collection of the training data, i.e., data which is well-

distributed, sufficient, and accurately measured-

simulated, is the basic requirement to obtain an

accurate model. In this work, it is generated a number

of input-output patterns at different loadingconditions. The different loading conditions in thesystem are achieved by varying the active and

reactive power loads in the system within a certain

range with respect to the base operating condition.

In this work the active and reactive power loads are

varied, with uniform power factor, in such a way that

the new load condition always remains within a range

of 60 120% of the base operating condition of the

system under consideration. The inputs to the

proposed RBFN are the real and reactive power

demands of the system. The outputs are the transfer

capability between two areas, and the voltage

magnitudes and voltage angles in those areas. Theinput-output patterns for training the proposed ANN

are generated from the proposed repeated power flow

algorithm. The data used for training the ANN is

normalized. The input-output patterns used for

training the ANN is given in the next chapter.

Summary of RBF Learning AlgorithmStep 1: Calculate the centres and their widths using

input data set.

Step 2: Calculate the output of the basis function

(hidden layer)

Step 3: update the weight

Step 4: Repeat 2-3 for each pattern in the input data

set.

Step 5: Repeat 2-4 until the cost function is

acceptably small, training stops, or some other

terminating condition occurs.

Transfer Capability Calculations Using Repeated

Power Flow Method

The Repeated Power Flow (RPF) method, which

repeatedly solves power flow equations at a

succession of points along the specified

load/generation increment, is used in this paper for

TTC calculation. The algorithm of the repeated

power flow method is given above, using this; a

transfer capability program is developed in

MATLAB environment. The transfer capabilitiesbetween the system areas, for different load

conditions (60 120%of the base operatingcondition of the system), have been computed by

applying this transfer capability program. The

simulation results for base operating conditions are

given in Table 1.

The voltage magnitude and the voltage angles at

different buses for the areas under consideration also

have been calculated by performing the proposed

transfer capability program. The procedure is

repeated for different load operating conditions.

Table 1 Transfer Capabilities for a base operating

condition

Areas Transfer capability(MW)

From area 1 to area 2






6.0000

54.8338

24.0050

19.0300

18.4520

6.0000

Radial Basis Function eural etwork Based

Transfer Capability Computations

In this paper, the radial basis function network(RBFN) model, discussed in the previously, is

utilized for calculating the total transfer capabilities

between the different system areas. The two areas

considered here are area 2 and area 3. Transfer

capability from area 2 to area 3 has been computed

using the proposed approach.

The input-output patterns for training the proposed

ANN are generated from the proposed repeated

power flow algorithm. The inputs to the proposed

RBFN are the real and reactive power demands of the

system. The outputs are the transfer capability

between two areas, and the voltage magnitudes and

voltage angles in those areas. In this paper, it is

generated a number of input-output patterns at

different loading conditions. The different loading

conditions in the system are achieved by varying the

active and reactive power loads in the system within

a certain range with respect to the base operatingcondition. The data used for training the ANN is

normalized. The number of epochs taken for training

the system is 17 for achieving the error goal of 10-6

with a spread constant of 0.114. The simulation of

was carried out in MATLAB. The convergence of theRBFN is shown in Fig.4 Table 2 shows the

comparison of transfer capabilities from area 2 to

area 3 obtained with RBFN method against the RPF

method for different load operating conditions. Table

3 shows the comparison of the voltage magnitudes,

voltage angles of area 2 obtained with RBFN method

against conventional methods for the transfer

capability case of area 2 to area 3 for 85% base

operating condition. The relative error is defined as

follow.

%100Xt

toerrorrelative

i

ii =


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Where ti is the exact value from repeated power flow

solutions and oi is the output of RBF Neural network

Fig. 4 Convergence of the RBFN to the performance

goal of 1e-6

The computation time requirement of the RBFN is

small as compared to the conventional RPF method

and is given in the table 4. The simulation of both

these was carried out in MATLAB on the Pentium 4

machine with 2.0GHz clock.

Table 2 Transfer capability from area 2 to area 3:

Comparison of RPF method and RBFN methodLoad

conditionTransfer capability(MW) Relative

Error

RPF Method RBF Method

85%

92.5%

97.5%105%

115%

117%119%

28.9047

26.4881

24.828622.3429

18.9771

18.293217.6094

28.9124

26.4783

24.829022.3431

18.9743

18.292917.6096

0.0266%

0.0369%

0.0016%0.0002%

0.0147%

0.0016%0.0013%

Table 3 Area 2 Bus Voltage Magnitudes Voltage

Angles:-Comparison of RPF method and RBFN

method (85%Base operating condition)

Table 4 Comparison of Computation time: RPF

Method versus RBFN Method

COCLUSIO

The significant contributions of this paper

are: Development of Repeated Power Flow(RPF) algorithm for the computation of

Transfer capabilities between system areas.

Application of Radial Basis Function NeuralNetwork (RBFN) for fast calculation of total

transfer capabilities.

Bus

o.

Bus Voltage

Magnitudes (p.u.)Relativ

e

Error

(%)

Bus Voltage

Angles (degree)

Relative

Error

(%)

RPF

Method

RBF

Method

RPF

Method

RBF

Method

12 0.9762 0.9762 0.000 -0.5207 -0.5250 0.825

13 1.0000 1.0000 0.000 2.5210 2.5167 0.170

14 0.9591 0.9591 0.000 -1.3006 -1.3052 0.353

15 0.9665 0.9665 0.000 -1.2197 -1.2243 0.377

16 0.9639 0.9639 0.000 -1.2920 -1.2973 0.410

17 0.9671 0.9671 0.000 -1.5508 -1.5570 0.399

18 0.9436 0.9437 0.010 -2.2742 -2.0932 0.010

19 0.9400 0.9400 0.000 -2.5863 -2.5917 0.208

20 0.9463 0.9463 0.000 -2.3640 -2.3693 0.224

23 1.0000 1.0000 0.000 -0.3131 -0.3177 1.469

Method Computation Time

(ms)

RPF Method

RBFN Method

425

90

-

3

-

2

-

1

1

12 1314 15 16 17 18 19 20 23

Bus

Number

Voltage

angle

RP

FRBFN

Fig.5 Area 2 Bus Voltage AnglesComparison of RPF and RBFN method(85%Base operating condition)

-

-

10 21 22 24 25 26 27 29 30

Bus Numbers

Voltage

Angle

(degree)

RP

RBF

Fig.6. Area 3 Bus Voltage AnglesComparison of RPF and RBFN method(85%Base operating condition)


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The results obtained with RBFN based approach are

practically matching with those obtained with the

conventional RPF method. Further RBFN is observed

to give significant reduction in computation time,

thus making it a potential candidate for online

application.

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SYMBOLSat bus i

Sijmax-Maximum allowed apparent power flow

Pr -The interchange real power sending areas to

receiving areas

K-Bus not in receiving area

m- Bus in receiving area

Pkm-Tie line real power flow (from bus k sending

areas to bus m in receiving area)

R -Set of buses in receiving area

-Set of all the buses

Yij -Magnitude of ijth element of Admittance of

matrix Y

ij- Angle of ijth element of Admiittance of matrix

Y

Vi - Magnitude of voltage at bus i

i -Voltage angle at bus i

Pg- Real power output of generator

Qg- Reactive power output of generator

Pi -Net real power at bus i

Qi -Netreactive power at bus i

Sij-Apparent power flow of transmission line

Pgmin-Minimum real power output of generator

Pgmax-Maximum real power output of generator

Qgmin-Minimum reactive power output of generator

Qgmax-Maximum reactive power output of generator

Vimin,-Minimum of voltage magnitude at bus i

Vimax -Maximum of voltage magnitude

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