Download Online Reactive Power Determination For Voltage Stability

Online Reactive Power Determination For Voltage
Stability Enhancement Using AI Techniques
A.KARUPPA SAMY, PG Student
Dr. S. JEYADEVI, Professor,
Department of EEE,
Kamaraj College of Engineering and Technology,
Virudhunagar, India
[email protected]
Department of EEE,
Kamaraj College of Engineering and Technology,
Virudhunagar, India
[email protected]
Abstract: - This paper develops a fuzzy based online tool to
determine the minimum VAR support required for a projected
load demand with a view to ensure voltage stability in a power
system. The most vulnerable load buses of the system from
voltage stability point of view have been identified by Voltage
Stability Index. The fuzzy tool is developed based on the
estimated VM and VSI at the critical bus using the ANN model.
A separate feed forward and Radial basis type of ANN is trained
for vulnerable load bus. For each of these ANN’s, different
inputs, comprising of the moments obtained by multiplying the
real power and reactive power contributions the real and
reactive power loads and the voltage magnitude at the
vulnerable load bus. The target output for each input pattern is
obtained by computing the L-index value. The tool incarnates a
methodology through which the operator can initiate steps to
improve the voltage profile and bring the system far away from
the point of voltage collapse.It has been applied to the IEEE 14
bus test system to exhibit the viability and effectiveness of the
proposed method.
Keywords: Voltage Stability, L-index, Multi Layer
Feed Forward, RBFNN.
I. INTRODUCTION
The existing resources in present day power systems
are inadequate to meet the ever-growing load demand and as a
result the grids are operated closer to the voltage stability
boundaries. The system is therefore prone to voltage collapse
even for a small increase in load demand. Voltage stability has
become an increasingly important factor in the operation and
planning of electric power systems. Voltage stability has been
the keen interest of industry and it is generally triggered by
some form of disturbance or change in the operating
conditions that create an increased demand for reactive power
that is in excess of what the system is capable of supplying [12].
VS margin is directly assessed using a plot of the PV
curve obtained from a series of load flow solutions based on
continuation method or repeated power flow method [3-4]. The
other method is to avail the use of an index from a reduced load
flow Jacobian matrix computation such as a minimum singular
value, minimum magnitude of Eigen value and determinant [5–
6]. It provides an indirect relative measure of proximity to
voltage instability.
It is well known that a trained ANN is a very suitable
tool for on-line use over the other computationally expensive
methods. There have been some attempts to use ANN for
online voltage stability assessment [7-8]. EI-Keib and X Ma
propose the energy function approach for voltage stability
assessment and come out with voltage stability margin at the
system level [7].
In the last three decades, a number of interesting
applications of fuzzy logic have been found in the area of
power systems, such as load forecasting, power system
stabilizer design and reactive power control [11] because of
its usefulness in reducing the need for complex mathematical
models. Fuzzy logic employs linguistic terms which deal with
casual relationships between the input and output variables. It
becomes easier to manipulate and rig out solutions,
particularly where the mathematical model is not explicitly
known or is difficult to solve.
The system operators of present day power systems
need online tools that can enhance their understandings of
where the system is operating, how the system behaves for a
projected load demand from VS point of view and how the
operating conditions can be enhanced to avoid VC. This
paper is thus directed towards developing a fuzzy based
online tool that uses the ANN model suggested in [10] to
determine the VAR support required to bring the system
away from the voltage instability region for a projected load
demand, as the unavailability of sufficient reactive power
appears to be the prime reasons for VC.
The network was trained using radial basis function
neural network (RBFNN), which is a powerful function
approximator. The error value is compared with the MultiLayer Feed Forward Network.
II. VOLTAGE STABILITY INDEX
VS analysis involves determination of an index called
VSI, which is an approximate measure of closeness of the
system to VC. Among the available methods of determining
the VSI, the index suggested in [5], called L-index, is popular
among the researchers. Its value ranges from 0 (no load
condition) to 1 (voltage collapse). The bus with highest value
inclines to be the most vulnerable bus in the system. The
calculation of this VSI is briefly outlined below.
The relationship between voltage and current for a power
system can be expressed as
𝐼
𝑌
[ 𝐺 ] = [ 𝐺𝐺
𝐼𝐿
𝑌𝐿𝐺
𝑌𝐺𝐿 𝑉𝐺
][ ]
𝑌𝐿𝐿 𝑉𝐿
(1)
Rearranging the above equation,
𝐼
𝑌
[ 𝐺 ] = [ 𝐺𝐺
𝐼𝐿
𝑌𝐿𝐺
𝑌𝐺𝐿 𝑉𝐺
][ ]
𝑌𝐿𝐿 𝑉𝐿
Where, [𝐹𝐿𝐺 ] = – [𝑌𝐿𝐿 ]−1 [𝑌𝐿𝐺 ]
(2)
(3)
𝑦𝑘 (x) = ∑ℎ𝑗=1 𝑤𝑘𝑗 ɸ𝑗 (x)+ 𝑤𝑘0
The VSI of jth bus is given by,
𝑉𝑆𝐼𝑗 = |1 −
∑𝑖Ԑ𝛼𝐺 𝐹𝑖𝑗 𝑉
𝑖
𝑉𝑗
| j ϵ αL
(4)
The values of Fji are obtained from the matrix FLG. The
VSI for a given load condition are computed for all load
buses and the maximum of the indicator values gives the
proximity of the system to VC. This maximum value is a
quantitative measure for the estimation of the distance of the
actual state of the system to the stability
limit.Where,
αL - set of load buses.
αG - set of generator buses.
𝑉𝑗 - complex voltage at bus-j
𝑉𝐺 , 𝑉𝐿- voltages at the generator and load buses respectively.
𝐼𝐺 , 𝐼𝐿 - Currents at the generator and load buses respectively.
𝑌𝐺𝐺 , 𝑌𝐺𝐿 ,𝑌𝐿𝐺 and𝑌𝐿𝐿 - sub matrices of bus admittance
matrix
III. REVIEW OF RADIAL BASIS FUNCTION NETWORK
Radial basis function network [9] is a class of single
hidden layer feed forward neural network. Fig. 1 shows the
schematic diagram of a RBF neural network. The input nodes
pass the input directly and the first layer connections are not
weighted.
Where 𝑤𝑘𝑗 the connection weight between the kth is
output node and jth hidden node and 𝑤𝑘0 is the bias term.
RBF networks can be viewed as an alternative tool for
learning in neural networks. While RBF networks exhibit the
same properties as back propagation networks such as
generalization ability and robustness, they also have the
additional advantage of fast learning and ability to detect
outliers during estimation. The attractive feature of RBFNN
lies in the linear dependence in the parameters which greatly
simplifies the design and analysis of such networks. It also has
an advantage of easy and effective learning algorithm
compared to other MLPNN.
IV. PROPOSED METHODOLOGY FOR VAR
ESTIMATION
The aim of the present work is to develop an online
tool for estimation of VAR support required to be provided in
the system for a projected load demand, when the system
operating conditions are closer to voltage instability limit. It is
an accepted fact that the enhancement of VM and VS at the
most critical bus by VAR support improves the VP and VS of
the entire power system. In other words, the information
available at the most critical bus is an indication of how far the
system is away from the instability point.
Therefore the fuzzy tool is developed based on the
estimated VM and VSI at the critical bus using the ANN
model Most of these methods require large number of inputs,
which causes difficulty in training the network especially for
larger power systems. However, efforts are being taken to
reduce the number of input variables for ANN based approach.
Once trained, the execution time of ANNs subjected to any
input is very less, which makes it more suitable for on-line
voltage stability assessment compared to conventional
methods. The block diagram of RBFNN is shown in Fig.2.
𝑃𝑐𝑏
𝑄𝑐𝑏
𝑃𝑁𝐸𝑇
𝑄𝑁𝐸𝑇
Fig. 1. Schematic diagram of RBF neural network
The transfer functions in the hidden nodes are similar to
the multivariate Gaussian density function is given by eqn. (5)
ɸ𝑗 (x) = exp (
2𝜎𝑗2
VSI
RBFNN Model
𝑉𝑀
Fig. 2. Block diagram of RBFNN Model
A. VAR Estimation Tool
2
−‖𝑥−𝜇𝑗 ‖
(6)
)
(5)
Where x is the input vector, lj and rj are the center
and the spread of the corresponding Gaussian function. Each
RBF unit has a significant activation over a specific region
determined by μj and σj, thus each RBF represents a unique
local neighbourhood in the input space. The connections in the
second layer are weighted and the output nodes are linear
summation units. The value of the kth output node 𝑦𝑘 is given
by eqn. (6)
The Fuzzy tool is designed to compute the reactive
power support required to be provided in the system. The fuzzy
terms describing the input and output variables are as follows:
∆𝑉𝑆𝐼 = {𝐿, 𝐿𝑀, 𝑀, 𝐻𝑀, 𝐻}
∆𝑉𝑀 = {𝐿, 𝐿𝑀, 𝑀, 𝐻𝑀, 𝐻}
∆𝑄𝑐 = {𝐿, 𝐿𝑀, 𝑀, 𝐻𝑀, 𝐻}
The block diagram of the VAR Estimation Tool is
shown in Fig. 3. It is designed to compute the reactive power
support required to be provided in the system.
In fuzzy logic based approaches, the decisions are
made by forming a series of rules that relate the input variables
to the output variables using if–then statements. A set of
multiple-antecedent fuzzy rules is established for determining
∆𝑄𝑐. The inputs to the rules are ∆𝑉𝑆𝐼 and ∆𝑉𝑀 and the
output consequent is∆𝑄𝑐 . The rules are summarised in the
fuzzy decision matrix in Table I
TABLE I
FUZZY CONTROL RULES
∆𝑸𝒄
∆𝑽𝑴
L
LM
M
HM
H
LM
LM
L
L
L
M
LM
LM
L
L
M
M
LM
LM
L
HM
HM
M
M
LM
LM
H
H
HM
M
M
LM
AND
L
Fig. 3. Block diagram of proposed model
The fuzzy model treats ∆VSI and ∆VM as the inputs,
adjusts the reactive power support that in turn alters the
reactive power load in the ANN model till the system enters
into a safe region defined by threshold values of VM and VSI.
The Fuzzy Tool in fact estimates the change in reactive power
support ∆QC and the limit control logic updates the VAR
support required at the chosen critical bus 𝑄𝐶𝑐𝑏 subject to a
maximum of 𝑄𝐿𝑐𝑏 and the net VAR support required in the
system 𝑄𝐶𝑛𝑒𝑡 .
B. Designing of Fuzzy Controller
A one-dimensional triangular and trapezoidal
membership functions within the range of values for VSI and
VM respectively, for both the inputs and output variables are
shown in Fig. 4.
LM
∆𝑽𝑺𝑰 M
The input variables are related to the output variable,
after which the fuzzy results are defuzzified through what is
called a defuzzification process, to achieve a crisp numerical
value. The most commonly used centroid or centre of gravity
defuzzification strategy [12] is adopted. The ANN model
estimates the VM and VSI at the critical bus when the
projected load data is presented, after which the fuzzy logic
along with Q-limit control logic compute the required VAR
support to be provided to enhance the VS and VP of the
system.
C. Q-limit control logic
The VM and VSI are estimated by the ANN model for
the projected load demand. These estimated values are
compared with threshold values of VSI and VM and if both the
error components ∆VSI and ∆VM are less than or equal to
zero, then the system remains in stable for the projected load
demand. If any one or both of the error components are
positive, then the fuzzy logic determines the ∆Q and the
control algorithm updates either the local VAR support or
systems VAR support. The Q-limit control logic is define by,
𝑖𝑓 𝑄𝐶𝑐𝑏
Fig. 4. Membership function chosen for linguistic variables.
𝑄𝐶𝑐𝑏 = 𝑄𝐶𝑐𝑏 + ∆Qc
𝑄𝐶𝑛𝑒𝑡 = 𝑄𝐶𝑛𝑒𝑡 + ∆Qc
≥ 𝑄𝐿𝑐𝑏 , 𝑡ℎ𝑒𝑛 𝑠𝑒𝑡 𝑄𝐶𝑐𝑏 = 𝑄𝐿𝑐𝑏
The VAR support alter the input to the ANN network,
which in turns provides the improved VM and VSI. The
resulting error components may become zero or negative. If
they still remain positive, the above process is repeated till the
error components become zero or negative. The maximum
VAR compensation at the cb is limited to 𝑄𝐶𝑐𝑏 L for avoiding
over-compensation.
D. Proposed algorithm
V. RESULT & DISCUSSIONS.
The output obtained from the Load flow program for
different loading conditions are taken as the data base for
training the neural network. Output vector is the L-index for all
the buses. The network is trained for different samples for all
the buses as a cell array at a time for obtaining the target Lindices fed as the output for training. Once tested satisfactorily,
the trained network is used to find the L-indices online and
thus the stability margin, weakest bus and proximity of voltage
collapse. Fig. 5 shows the functional flowchart of the procedure
for developing the proposed model
START
Perform the load flow sub program and find the
Stability Indices using conventional algorithm
Prepare the input data base for various loading
conditions for the required input vector and
prepare the output database for the L-index
Normalize the input samples using the formula,
𝑥𝑜𝑙𝑑−𝑚𝑖𝑛𝑜𝑙𝑑
𝑥𝑛𝑒𝑤 =[𝑚𝑎𝑥
𝑜𝑙𝑑−𝑚𝑖𝑛𝑜𝑙𝑑
(𝑚𝑎𝑥𝑜𝑙𝑑−𝑚𝑖𝑛𝑜𝑙𝑑 ) ]+𝑚𝑖𝑛𝑛𝑒𝑤
Perform the NN algorithm for training two separate
ANN with selected Input Output vectors for both
Normal and different Loading conditions.
Develop the fuzzy model to obtain ∆QC
Invoke the Q-limit control logic
Combine the ANN model, fuzzy model and Q-limit
control logic. Choose threshold values for VSI and VM.
The model is ready for online estimation of VAR support
Calculate the amount of VAR needed to bring the
system to stable.
END
Fig. 5. Flowchart of the Reactive power Determination for
voltage stability enhancement.
The proposed approach is tested on IEEE 14 bus
system. Initially the fast-decoupled load flow followed by VSI
computations for all load buses are carried out for the base-case
load demands. Bus-14, whose VSI is the largest, is identified as
the most vulnerable bus. The normal case power flow result for
IEEE14 bus system is shown in Table II. The total power
drawn by the load is 259 MW and 73.5 Mvar.
TABLE II
BASE CASE POWER FLOW WITH L-INDEX
Bus No
P(Mw)
Q(Mvar)
VSI
-
Voltage
Mag
1.060
1
-
2
21.70
12.70
1.045
-
3
4
5
6
7
8
9
10
11
12
13
14
94.20
47.80
7.60
11.20
29.50
9.00
3.50
6.10
13.50
14.90
19.00
-3.90
1.60
7.50
16.60
5.80
1.80
1.60
5.80
5.00
1.010
1.018
1.020
1.070
1.062
1.090
1.056
1.051
1.057
1.055
1.050
1.036
0.0297
0.0203
0.0377
0.0664
0.0634
0.0361
0.0239
0.0318
0.0768
-
The threshold value for VM may be chosen closer to,
but in any case less than 1.0 per unit. The same for VSI is set
by a trial and error process. It depends on the power system
configuration and the operating state. If this value is chosen too
high, it does not ensure that the power system is maintained in
the stable state. On the other hand, if it is fixed too low, the
VAR support to be provided may be too excessive. The final
Threshold values to set VMT=0.95 and VSIT=0.185.
There are thus four inputs (𝑃𝑐𝑏 , 𝑄𝑐𝑏 , 𝑃𝑁𝐸𝑇 , 𝑄𝑁𝐸𝑇 ) and
two outputs (𝑉𝑀 , VSI) for the proposed ANN model to estimate
VSIs for the critical bus 14. The parameters of the ANN
controller used in the L-index Monitor design are shown in
Table III.
TABLE III
ANN PARAMETERS
Connections
Learning
No. of hidden Neurons
Training Algorithm
No. of training samples
No. of testing samples
RBFNN
Supervised
250
trainlm
250
50
As many as 300 training/testing patterns were generated
by changing the load at each bus randomly for the load
variation of 50% of the base case. Out of 300 patterns, 250
patterns are selected randomly for training and remaining 50
for testing of the RBFNN. In this case, better results were
obtained when only the real power loads at different buses
(total 17 in nos.) were selected as input features to the RBFN.
The proposed RBF model has one input layer of 17 neurons;
one hidden layer of 250 neurons (optimum no. of clusters or
hidden nodes) and an output layer of 18 neurons representing
the modified values of real power loads at different buses.
A. ANN Performance
To evaluate the performance of neural networks we have
used mean square error (MSE). Fig 6 Shows that the RBF
network performance during training. The best performance is
obtained, when neurons = 250, MSE = 0.00778637.
Fig. 6. Error Plot in Training
From Fig. 6 it is observed that, error value for all the
training samples are lie in the range of -0.1 to 0.2 and most of
the values are nearer to zero.
Fig 7 Shows that the RBF network performance during
testing. The best performance is obtained, when neurons = 31,
MSE = 4.64038e-19.
Fig. 7. Error Plot in Testing
From Fig. 6, it is observed that, error value for all
the testing samples are lie in the range of -0.2 to 0.2. Since
the testing samples are unseen, the error value of testing data
is slightly greater than the error value of training data.
However, the testing result analysis shows that the use of
ANN for monitor is quite appreciable.
B.ANN Output
The output of ANN to predict the L-index Value for
both base case and Maximum load condition is given in
Table IV and V.
TABLE IV
VOLTAGE STABILITY INDEX AT DIFFERENT
BUSES AT A NORMAL LOADING CONDITION
Bus
4
5
7
9
10
11
12
13
14
Target VSI
0.0297
0.0203
0.0377
0.0664
0.0634
0.0361
0.0239
0.0318
0.0768
Output VSI
0.0298
0.0205
0.0377
0.0663
0.0633
0.0361
0.0240
0.0318
0.0762
Error
0.0001
0.0002
0.0000
-0.0001
-0.0001
0.0000
0.0001
0.0000
-0.0006
Above table shows the L-index values at each bus
for the base case. From the above table it can be observed
that Bus-14 is more prone to voltage instability as its L-index
is nearer to unity compared to other buses. Stability of bus 5
is more as its L-index is low.
TABLE V
VOLTAGE STABILITY INDEX AT DIFFERENT
BUSES AT A MAXIMUM LOADING CONDITION
Bus
4
5
7
9
10
11
12
13
14
Target VSI
0.2315
0.2115
0.2925
0.4501
0.4032
0.2344
0.1971
0.3688
0.9222
Output VSI
0.2314
0.2114
0.2927
0.4508
0.4038
0.2345
0.1974
0.3691
0.9223
Error
-0.1000
-0.1000
0.2000
0.7000
0.6000
0.1000
0.3000
0.3000
0.1000
Above table shows that with the increase of load on
14th bus, the voltage stability index, L, increases and reached
to 0.9222 which is very near to unity value. From the above
table it can be observed that Bus-14 is more prone to voltage
instability as its L-index is nearer to unity compared to other
buses.
C. Comparison with Feed Forward Network:
VI. CONCLUSION
Table VI shows the comparison between the RBFNN
and MLFNN output. From this table, it is observed that RBF
networks take less time for training, but they require more
number of hidden nodes as compared to multilayer feed
forward networks.
TABLE VI COMPARISON OF RPFNN AND MLFNN
ANN
Modal
Hidden
nodes
Itera
tions
Training
Time (s)
Training
Error
Testing
Error
RPFNN
250
6
2.41
0.00778637
4.64038e-19
MLFNN
50
23
41.47
0.0855
0.0954
This shows that the proposed RBFNN is
computationally efficient and hence is suitable for on-line
voltage security assessment.
This paper has presented a radial basis function
network-based fast voltage security assessment method for
on-line applications. A fuzzy methodology has been
formulated to estimate the VAR support required to ensure
the voltage stability for a projected load in a power system.
Computer simulation was carried out on the IEEE 14-bus
system for voltage security assessment. The proposed
network can be quickly trained, as it involves only four inputs
for each critical bus. It has been framed with minimum
number of inputs to represent real and reactive power
demand, irrespective of the system size. The use of a trained
ANN model along with the fuzzy intelligence has been found
to add strength to the process of predicting the minimum
VAR support. By reducing the dimension of the input
features using feature selection the efficiency of the ANN
model has been significantly increased both in the learning
and estimation stages. Since the approach is very fast it can
prove to be more suitable for on-line tool in energy
management systems for VAR estimation to bring the system
to a safe VS region as compared to conventional optimization
techniques.
D. Fuzzy Tool Output:
The developed fuzzy model is combined with the
ANN model to constitute the Fuzzy Tool. The Fuzzy Tool is
then tested using projected input data that corresponds to
different loading patterns and the obtained VAR support for
five test cases of IEEE14 Bus system under work are given in
Table VII.
TABLE VII
RESULTS OBTAINED BY THE FUZZY TOOL
Test
Cases
1
2
3
4
5
Projected load input
𝑷𝒏𝒆𝒕
𝑸𝒏𝒆𝒕
𝑸𝒄𝒃
𝑳
𝑳
𝑳
0.200 0.070 2.650 0.900
0.400 0.150 3.000 0.950
0.250 0.120 3.300 1.200
0.500 0.200 2.900 1.200
0.300 0.100 3.100 1.600
𝑷𝒄𝒃
𝑳
VAR Support
𝑸𝒄𝒃
𝑸𝒄𝒃
𝑪
𝑪
0.000 0.000
0.124 0.124
0.120 1.049
0.200 1.114
0.100 1.725
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
The Fuzzy Tool quickly provides the reactive power
support required to that the critical bus and the system for
the envisaged load pattern. The VMcb and VSIcb before and
after providing the VAR support in the system. It is
observed from this table that the operating point for all test
cases except the first one in all the test systems is in the
critical region and requires immediate corrective actions to
bring the system to a safe operating zone. It is also noted
that in all the test cases the VAR support at the critical bus is
limited to the local reactive power demand.
It is summarised that the Fuzzy Tool ideally serves to
provide VAR compensation required to retain the system in
the stable region in addition to enabling estimation of VM
and VSI at the most vulnerable bus. The computations
involved are very less as it uses trained ANN model and the
firing of a few fuzzy rules. Therefore this model is ideally
suitable for online estimation of VAR support required to
sustain the system with in a safe region of VS.
[8]
[9]
[10]
[11]
[12]
Taylor CW. “Power system voltage stability”. McGraw-Hill,
Inc.; 1994.
Kundur P. “Power system stability and control”. McGraw-Hill,
Inc.; 1993.
Lee Ching-Yin, Tsai Shao-Hong, Wu Yuan-Kang. “A new
approach to the assessment of steady-state voltage stability
margins using the P–Q–V curve” Electrical Power & Energy
System 2010;32(10):1091–8.
Da Costa VM, Guedes MR, De Sousa Rosa AL, Cantarino M.
“A new modeling of loading margin and its sensitivities using
rectangular voltage coordinates in voltage stability analysis”
Electrical Power & Energy System 2010;32(4):290–8.
Kessel P, Glavitsch H. “Estimating the voltage stability of a
power system” IEEE Trans Power Delivery 1986;1(3):346–54.
Sinha AK, Hazarika D. “A comparative study of voltage
stability indices in a power system. Electrical Power & Energy
System 2000;22(1):589–96.
EI-Keib, X Ma, “Application of Artificial Neural Network in
Voltage Stability Assessment”, IEEE Trans. Power System,
Vol. 10, no 4, pp. 1890-1896, Nov 1995.
S.Kamalasadan, A. K. Srivastava, D. Tukaram “A new
intelligent algorithm for online voltage stability assessment and
monitoring” Electrical Power & Energy System 2009;24:100–
110.
Saikat Chakrabarti, Benjamin Jeyasurya, “Multi contingency
voltage monitoring of a power system using adaptive radial
basis function network” Electrical Power & Energy System
2008;30:1-7
G.Balamurugan, P.aravindhababu, “Online VAR support
estimation for voltage stability enhancement” Electrical Power
& Energy System 2013;49:408–413.
Momoh JA, Tomsovic K. Overview and literature survey of
fuzzy set theory in power systems. IEEE Trans Power Syst
1995;10(3):1676–90.
Cox L. The fuzzy systems handbook. 2nd ed. New York:
Academic Press; 1999