Prediction of Transmission Line Overloading Using Intelligent Technique

8/2/2019 Prediction of Transmission Line Overloading Using Intelligent Technique

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Chapter 1

INTRODUCTION

1.1Need of Prediction of overloading in transmission linesToday the Generation system has expanded enormously but the expansion of transmission

system has not kept pace with it. As a result the transmission system is overloaded, resulting

in high losses. The problem of monitoring the power flows and bus voltages in a power

system is very important in maintaining system security and fast prediction is essential for

controlling these quantities. As power systems have become more stressed due to increased

loading and large interconnections, there will be an increase in cases of voltage limit

violation and line loading limit violation, particularly in contingency conditions like line

outage, generator outage etc. The alleviation of emergency transmission line overload is a

critical problem in power system operation. An efficient, reliable and direct method is always

desirable. The concept of local optimisation is introduced, and a method is developed for the

same. This gives the proper sequence of control actions and adjustment in control variables to

alleviate line overloads [2]. This is essential that power flows in all the branches respect their

specified limits not only in base case condition but also in stressed/line outage conditions.

The most severe violation in a line flow limit can be due to different contingencies. Therefore

an immediate need arises to take corrective action for alleviation of line overloads in the

overloaded lines of the system.

There are several methods based on optimal power flow (OPF) for the corrective and

preventive control actions along with economy and security function. Power system is a

dynamic system as the operating state of it continually changes with respect to time. The

emergency state of line overloading may occur as a result of sudden increase in system

demand, outages of generator or transmission line or failure in any of the system components.

1.2Literature survey

In reference [3], a corrective switching algorithm has been proposed which relieves overloads

and voltage violations as well. The traditional form of load control (shedding) is quite

disruptive to consumers and so often avoided. In reference [4], a non-disruptive load control

method has been developed to switch small pieces of load, so that interruptions are

effectively unnoticed by consumers.

Several power flow methods are available to compute line flows in a power system like

Gauss Seidel iterative method, Newton-Raphson method, fast decoupled power flow method

and dc power flow method but these are either approximate or too slow for on-lineimplementation [5,8].


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In [6] an approach based on radial basis function neural network (RBFN) is presented for

corrective action planning to alleviate line overloading in an efficient manner. Effectiveness

of the proposed method is demonstrated for overloading alleviation under different

loading/contingency conditions in 6-bus system and 24-bus RTS system.

1.2.1 Role of Artificial neural networks in Power Systems

Due to the uncertainty in the results now a days methods have been developed that use

artificial intelligence (ANN, fuzzy logic). These methods are accurate and efficient in

discovering similarities among large bodies of data and synthesizing fault tolerant model for

nonlinear, partly unknown and noisy/corrupted system.

Artificial neural network is the functional imitation of a human brain which simulates the

human intuition in making decisions and drawing conclusions even when presented with

complex, noisy, irrelevant/partial information. The information going to the input layer

neurons (units) of artificial neural network is recoded into an internal representation and the

outputs are generated by the internal representation rather than by the input pattern. It can

model any non-linear function without knowledge of the actual model structure and during

testing phase it gives the result in very short time. A neural network consists of a number of

neurons, which are the elementary processing units that are connected together according to

some pattern of connectivity. The development of artificial neural network involves into two

phases, training or learning phase and testing phase. Developing a neural network is unlikedeveloping software, because the network is trained, not programmed. Most of the published

work in power system area utilizes multi-layer perceptron (MLP) model based on back

propagation (BP) algorithm, which usually suffers from local minima and over fitting

problems [6].

1.3Organisation of this reportIn this report, a cascade neural network based approach is proposed for fast identification andprediction of transmission line overloading. The developed cascade neural network is a

combination of an Identification module (ANN1) and a Prediction module (ANN2). All the

training patterns are applied to the identification module, which is trained to classify them

either in overloaded class or in under-loaded class using a modified BP algorithm. The

identified overloaded cases are then passed to the prediction module (which is a feed-forward

counter propagation neural network) for prediction of line overloading.

The input features for CNN are taken from the set of real power injections at generation (PV)

and load (PQ) buses, and reactive power injections at PQ type buses as these independent and

known variables (prior to power flow analysis) influence the line flows most. Due to large


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number of such variable in any practical power system, it is not possible to consider all these

variables as inputs to an ANN, as it will increase the input dimension, the size of the neural

network i.e. the number of interconnection weights and ultimately the training time. So to

overcome this difficulty, the variables are grouped into different clusters and from each

cluster one representative variable is selected as the input feature to the proposed neuralnetwork. In this paper, angular distance based clustering [7] is applied for the selection of

input features.

Optimal training of the CNN has been achieved by iteration wise monitoring the error

patterns for the training set and the validation set. The proposed neural network based

technique is applied for overloading identification and prediction at different loading/

generation conditions in IEEE-14 bus system.

Chapter 2 presents the methodology used for the prediction of overloading in transmission

lines with the help of CNN. Chapter 3 presents the Simulation results and graphs representing

the results.


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Chapter 2

PROPOSED METHODOLOGY

The block diagram of the proposed Cascade neural network is shown in Fig. 2.1. By

perturbing the load at all the buses randomly in wide range of system operating conditions, a

large number of load patterns have been generated and full ac power flow analysis has been

carried out for each case to calculate real line-flow in each line of the power system. Angular

distance based clustering [7] is applied for selection of input features from the set of real

power injections at generation and load buses, and reactive power injections at load buses.

Output (0.1/0.9) 0.1

Input (Under-loaded)

0.9 (Overloading)

(Overloaded)

Input

Fig. 2.1 Cascade neural network for identification and prediction of overloading

An identification module which is a three-layered feed-forward neural network with singleclamped output as shown in Fig. 2.2, is developed to classify the transmission lines condition

either in overloaded or in under-loaded class taking into consideration the real power flows

and the maximum power flow limits in different lines.

Fig. 2.2 Identification module (three-layered ANN).

Identification

Module

Prediction

module


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The identification module is trained using modified BP algorithm [8] such that its target

output is high (0.9) when presented with a sample from overloaded class (C1), and low (0.1)

when presented with a sample from under-loaded class (C2). During training, the outputs of

the identification module greater than 0.9 are clamped to 0.9, similarly outputs smaller than

0.1 are clamped to 0.1 to reduce the likelihood of the network getting stuck in local minima.

The training set for identification module contains many more exemplars for under-loaded

class C2 than for class C1. When training a multilayer feed-forward neural network with

standard back-propagation for such a two-class problem, in which one dominant class

contains far more exemplars than a subordinate class (i.e., the training set is imbalanced),

the rate of convergence of net output error is very low.

Fig.2.3 Relationship between gradient vectors

The reason for this is that negative gradient vector computed by back-propagation for an

imbalanced training set does not initially decrease the error for the subordinate class as shown

in Fig. 2.3. Consequently in the initial iteration, the net error for the exemplars in the

subordinate class increases significantly. The subsequent rate of convergence for the

exemplars of the subordinate class is very low. To solve this problem, in place of standard BP

algorithm, a modified BP algorithm [8] is used that calculates a direction of the descent

vector v in weight space, which is downhill for class C1 as well as for class C2 in each

iteration as shown in Fig. 2.4 i.e. v satisfies

() () (2.1)where () and () refer to the errors (sum of squared errors) for the patternsbelonging to class C1 and class C2 respectively at Kth iteration.


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Fig. 2.4 Direction of gradient vectors in modified algorithm

Direction ofv is set so that it bisects the angle between

()and

():

()() ()

() (2.2)and thus the rate of learning can be accelerated by one order of magnitude for such two class

problems [8].

The prediction module is a feed forward counter propagation neural network (CPNN), which

uses a different mapping strategy namely counter propagation. The counter propagation

network provides a practical approach for implementing a pattern-mapping task, sincelearning is fast in this network[10]. The counter propagation neural network is shown in Fig.

2.5. This neural network model is a combination of Kohonen network and a Grossberg

outstar. The CPNN model (Fig. 2.5) involves both supervised and unsupervised learning.

The Kohonen network implements the winner-take-all (competitive) strategy for the weights

from the units in the input layer to the units in the hidden layer, and the Grossberg outstar

maps the winning neuron into the desired output. The unsupervised and supervised training

are applied to train the CPNN model.

Fig. 2.5 Feed-forward counterpropagation network.


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CPNN is trained in a two-phase process. In the first phase, the Kohonen layer neuron weights

are adjusted to match the input. The second training phase helps to adjust the Grossberg

weights in order to fit the desired neuron output. A large number of load patterns are

generated randomly by perturbing the load at all the buses and generation in wide range.

Newton-Raphson (NR) ac power flow program is developed to generate training/ testing

patterns for different load scenarios such that some of the transmission lines get overloaded.

2.1 Line overloading calculations using Newton-Raphson power flow

method

The objective of power flow or load flow study is to determine the voltage and its angle at

each bus, real and reactive power flows in each line and line losses in the power system forspecified power system conditions. The power flow studies are conducted for the purpose of

planning (viz. short, medium and long range planning), operation and control. For the

purpose of power flow studies, it is assumed that the three-phase power system is balanced

and also mutual coupling between elements is neglected [12-13]. Variables associated with

each bus of a power system include four quantities viz. voltage magnitude Vi, its phase angle, real power Pi and reactive power ; total 4m variables for m buses system. At every bustwo variables are specified, the remaining two can be found by solving the 2m power flow

equations. Depending upon which two are specified, the buses are classified as Swing Bus or

Reference Bus, Generator Bus or PVBus and Load Bus or PQ Bus.

From the nodal current equations, the total current entering the ith bus of m bus system is

given by

(2.3)Where is the admittance of the line between buses i and kand is the voltage at bus k. Inpolar coordinates

(2.4) (2.5) || (2.6)

Here, is the angle of the bus voltage and is bus admittance angle. At ith bus, complexconjugate power will be

(

)(2.7)

Or


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|| () (2.8)The real power at ith bus will be

|| () (2.9)Or

|| ( ) (2.10) ( ) ( ) (2.11)Similarly, the reactive power at ith bus will be

|| () (2.12)Or

|| ( ) (2.13) ( ) ( ) (2.14)Eqs. (2.10, 2.11) and (2.13, 2.14) are known as static power flow equations (SLPE).

The power flow equations used in Newton-Raphson method for computation of voltage

corrections are given as

[] [ ] [ ] (2.15)where,H, N, JandL are the sub-matrices of the Jacobian in Eq. (2.15), having ikth elements

as

(2.16)

Eq. (2.15) may be written as

[

] [ ]

[]

(2.17)


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The solution of Eq. (2.17) provides the correction vector i.e. for all the PVand PQ typebuses and s for all the PQ type buses, which are used to update the earlier estimates ofsand Vs. This iterative process is continued till the convergence is obtained i.e. mismatch

vector s for all the PVand PQ type buses and s for all the PQ buses become less than apre assigned tolerance value . Once the solution of bus voltages (|| and for load busesand for generation buses) is found, the power flows in line between buses i and kcan becalculated using nominal-pi representation of the line. Current flow from bus i towards bus k

will be

(2.18)where is line charging of the line between buses i and k. The power flow in the line i-katthe bus i is given by

(2.19)In Newton-Raphson method, Jacobian elements are to be calculated and its inverse is also

required using Eqs. (2.15) and (2.17) in each iteration. Due to this fact, the Newton-Raphson

method requires more time per iteration. However, this method provides accurate results and

is the most reliable ac power flow method. Hence, in this work the NR power flow program

has been developed and run to calculate real power flows in different lines of a power system.

Line overloading is evaluated as the amount by which the real power flow exceeds the

maximum power flow limit for the line i.e. the line rating.

Line overloading = real power flow in the line - rating of the line

Or

(2.20)Where is line overloading in any line i-kand is maximum power flow limit of linei-k. In case of overloading in any line i-k, the value ofwould be positive, otherwise itwould be either negative or zero.The solution algorithm for prediction of line overloading can be summarized in following

steps:

(i) A large number of load patterns are generated randomly by perturbing the load at all the

buses and real power generation at the generator buses.

(ii) Full ac power flow programs are run for each case to compute real power flows.

(iii) Input features are selected by using angular distance based clustering from the set of real

power injections at PVand PQ buses, and reactive power injections at PQ type buses.

(iv) The input data are normalised between 0.9 and 0.1.

(v) The normalised input data along with the topology (normalised Gij andBij corresponding

to the line between buses i andj) are used for training of the cascade neural network.


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2.2 Input Feature selection

In any ANN application, if a large number of inputs are used, the size of a neural network and

the number of interconnection weights will increase and the training of neural network will

be extremely slow. To avoid this problem, some feature selection technique is to be appliedso that only those inputs could be selected which strongly affect the output of a neural

network. Several feature selection methods like entropy reduction method, principal

component method, correlation coefficient based method, angular distance based method etc.

are available in the literature. However, in this paper, angular distance based clustering of

real and reactive power injections has been applied for input feature selection.

The basic purpose of clustering [7] is to group the total M system variables (SV1, SV2, . . .,

SVM) into G clusters such that the variables in a cluster have similar characteristics. One

representative variable from each cluster is picked out as a feature for the cluster. Thus the

number of variables will be reduced from Mto G. The system variables considered here are

real power injections at all the buses except slack bus and reactive power injections at PQ

buses only.

A large number of patterns (say N) are generated by perturbing the load at all the buses and

real power generation at the PVbuses randomly in wide range of operating conditions and

Newton-Raphson power flow as discussed in Section 2.1 has been run to obtain line flows for

each case. Each operating point i.e. the power injections can be described by state vector,

(i = 1, 2, . . ., N). All the Nstate vectors can be represented in the

form of a matrix Xas-

The ith row of matrix X contains the values for Msystem variable (SV1, SV2, . . ., SVM) at

ith operating point while jth column of matrix X consists ofSVj variables in theN training

patterns. In matrix X, if we define a column vector,

(2.21)Then the Msystem variables SVj (j = 1,2, . . .,M) can be clustered based on these column

vectors CYj. These system variables with similar vectors CYj will be grouped in one cluster.

In the angular distance based clustering [7] technique of feature selection, the system

variables are clustered on the basis of angular distance between them. The cosine value of the

angle between two vectors CYj and CYk is defined as

|| (2.22)


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Two vectors CYj and CYk, which are similar to each other, will have a small angle between

them. Hence, the cosine value as obtained by Eq. (2.22) can be used to evaluate the degree of

similarity between two vectors. Ifcos is greater than a specified threshold, the two vectorsCYj and CYk are considered as two similar vectors and are put in the same group (cluster).Otherwise a new cluster is formed for the vector CYk. The clustering process is carried out for

all the system variables. Once all the variables are processed, the algorithm is repeated until

stable clusters are formed. For any cluster g, the representative variable is selected by finding

out a system variable SVg whose vector is closest to the cluster vector Cg. The system

variable SVg will be feature variable for the cluster g. Thus, G features can be selected out of

Msystem variables. In this way, the input features i.e. the real and reactive power injections

are selected for training of the cascade neural network.


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Chapter 3

SIMULATION RESULTS

The cascade neural network based method has been tested for prediction of overloading in

IEEE 14-bus system [12], which is composed of 14 buses and 20 lines. Changing the load at

each bus and generation at PV buses randomly several load patterns were generated. The

power factor of loads at different buses was maintained constant. The NR power flow method

was used to compute power flows for each loading scenario. The input as well as output data

were normalised between 0.9 and 0.1. Since only one neural network is trained for a number

of line-flows, a topology number is required along with the input data to train the neural

network. The topology number in the form ofGij andBij corresponding to the line betweenbuses i andj are used for training of the identification module.

To reduce the training time the adaptive learning rate was also used along with modified BP

algorithm in identification module [8]. The data for IEEE-14-bus system were taken from

[12] with buses renumbered to make bus-1 as slack bus, buses 25 as PVbuses and buses 6

14 as load (PQ) buses. As many as 120 load scenarios were generated by changing the load at

each bus and generation randomly in wide range (50% of base case) and the full ac powerflow was run for each load pattern to compute the real line flows in different lines of the

sample system. Using angular distance based clustering, 10 no. of power injections (P2, P3,

P4, P6, P9, P13, P14, Q9, Q10, Q11) were selected with the threshold as 0.927. Inaddition to these features the line parameters G and B are also included as inputs, making the

total 12 inputs for CNN. All these input data were normalised between 0.1 and 0.9 to

overcome the problem of data suppression by large valued inputs. In this paper, each input

parameter X is normalized as Xn according to the following equation:

(3.1)Whereis maximum value ofXand is minimum value ofX.Each load scenario will generate 20 patterns corresponding to line flows in 20 lines and will

provide 2400 patterns. Out of 120 load scenarios, 80 load scenarios (1600 patterns) were

arbitrarily selected for training while, 20 load scenarios (400 patterns) were used as validation

set and the remaining 20 load scenarios (400 patterns) were used for testing the performance

of the identification and prediction modules. This validation set is used for checking the

optimal training point of the developed CNN.


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Outputs of the proposed identification module will identify the overloaded lines. If a line is

overloaded under some loading condition, it would be classified in overloaded class and the

corresponding output will be 0.9, otherwise it will be 0.1 for under-loaded class.

The proposed identification module ANN1 (12-27-1) has the input layer of 12 neurons; onehidden layer of 27 neurons (optimum number of hidden nodes) and an output layer of 1

neuron. The identification module was trained using a modified BP algorithm to filter out

(identify) the overloaded lines. The initial value of adaptive learning rate was selected as 0.5

which was changed during the neural network training according to the nature of training

error in each iteration. These identified line overloaded cases were applied for training of the

other ANN namely the prediction module for prediction of amount of overloading in those

lines.

Table I

Identification of overloading for IEEE 14-bus system

Line No. From bus To bus Target T ANN O Class

1 1 2 0.9 0.8949 OL

2 1 8 0.1 0.1971 UL

3 2 3 0.9 0.8957 OL

4 2 6 0.9 0.8773 OL

5 2 8 0.9 0.8585 OL

6 3 6 0.1 0.1015 UL7 4 11 0.1 0.1042 UL

8 4 12 0.1 0.1089 UL

9 4 13 0.1 0.1049 UL

10 6 7 0.9 0.8430 OL

11 6 8 0.1 0.1033 UL

12 6 9 0.1 0.1016 UL

13 7 5 0.1 0.1011 UL

14 7 9 0.1 0.1023 UL

15 8 4 0.9 0.8645 OL16 9 10 0.1 0.1017 UL

17 9 14 0.1 0.1034 UL

18 10 11 0.1 0.1043 UL

19 12 13 0.1 0.10407 UL

20 13 14 0.1 0.1146 UL

In the above table-T: Desired output of identification module; O: actual output of identification

module; OL: Overloaded Class; UL: Under-loaded class.


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Out of 1600 training patterns, the identified overloading cases were 586 corresponding to 80

load scenarios. These 586 patterns were used to train the prediction module ANN2 i.e. the

Counter propagation network (12-85-1). The initial values of as selected as 0.7 andconsequently decreased to 0.2. The initial value of b was selected as 0.1 and consequently

reduced to and 0.01.

During testing phase, the 400 unseen patterns were tested for screening through the trained

identification module. The trained identification module identified all the 147 overloading

cases correctly. These 147 overloading cases corresponding to 20 operating scenarios were

then passed to the trained prediction module for testing.

Though the proposed cascade neural network identifies all the testing patterns correctly and

predicts overloading amount accurately, the test results corresponding to only one load

scenario are presented in Tables I and II.

Table II

Determination of overloading for IEEE 14-bus system

Line No. From bus To bus Target ANN Error(pu)

1 1 2 0.6157 0.6163 -0.0006

3 2 3 0.2695 0.2712 -0.0017

4 2 6 0.3886 0.3898 -0.0012

5 2 8 0.3408 0.3391 -0.001710 6 7 0.1714 0.1737 -0.0023

15 8 4 0.2313 0.2352 -0.0039

Table I shows the performance of the identification module, which screens line flows in

overloaded or under-overloaded class while Table II presents the overloading amount in

overloaded lines screened by the identification module. As can be observed from Table I, the

identification module screens all the overloading cases correctly. Table II shows that actual

values of overloading amount and those obtained by the prediction module (ANN2) are veryclose to each other.


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Fig. 3.1 Testing Performance of ANN 2

The performance of prediction module for all the unknown overloading patterns is shown in

Fig. 3.1. The rms error for all the test patterns is 0.0043 p.u. The trained Cascade neural

network is able to identify all the overloading cases correctly and at the same time able to

predict the overloading accurately.


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Chapter 4

CONCLUSIONS

The identification of overloaded lines and prediction of line overloading in different

overloaded transmission lines are essential for secure and reliable operation of a power

system. For this purpose analytical methods take a long time, as ac power flow analysis has to

be carried out for any change in loading/generation condition. On the other hand, once the

training of the cascade neural network is successfully accomplished, the identification of

overloaded lines and prediction of overloading amount in those lines for unknown loading

conditions is almost instantaneous.

Once the overloading in different lines is predicted accurately, a fast and intelligent controlaction can be taken in the form of generation scheduling/load shedding to reduce the line

overloads to the security limits. The proposed intelligent technique can be implemented for

on-line MW security assessment in Energy Management Systems.


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BIBLIOGRAPHY

[1] Savita Sharma, Laxmi Srivastava, Prediction of transmission line overloading usingintelligent technique, Applied Soft Computing 8 (2008) pp-626633.(Base Paper)

[2] Shandilya, H. Gupta, J. Sharma, A method for generation rescheduling and loadshedding to alleviate line overloads using local optimisation, IEE Proceedings on

Generation, Transmission and Distribution 140 (5) (1993) pp-337342.

[3] S. Wei, V. Vittal, Corrective switching algorithm for relieving overloads and voltageviolations, IEEE Transactions on Power Systems 20 (4) (2005) pp-18771885.\

[4] I. Hiskens, B. Gong, MPC-based load shedding for voltage stability enhancement,in: Proceeding of the 44th IEEE Conference on Decision and Control, Seville, Spain,

December 1215, (2005), pp-44634468.

[5] N. Kumar, R. Wangneo, P.K. Kalra, S.C. Srivastava, Application of artificial neuralnetwork to load flow, in Proceedings TENCON91, IEE Region 10 International

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[6] Daya Ram, Laxmi Srivastava, Manjaree Pandit, Jaydev Sharma, Corrective actionplanning using RBF neural network, Applied Soft Computing 7 (2007) pp-10551063.

[7] Y.Y. Hsu, C.R. Chen, C.C. Su, Analysis of electromechanical modes using anartificial neural network, IEE Proceedings Generation, Transmission and

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[8] A.N. Adupa, G.K. Purushothama, K. Parthasarathy, D. Thukaram, A fuzzy controlfor network overload alleviation, International Journal of Electrical Power & Energy

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[9] R. Anand, Kishan G. Mehrotra, C.K. Mohan, S. Ranka, An improved algorithm forneural network classification of imbalanced training sets, IEEE Trans. Neural

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Prediction of Transmission Line Overloading Using Intelligent Technique

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