Available online at www.sciencedirect.com
Procedia Engineering 00 (2011) 000–000
Procedia Engineering 30 (2012) 53 – 60
Procedia Engineering www.elsevier.com/locate/procedia
International Conference on Communication Technology and System Design 2011
Power System Voltage Stability Assessment through Artificial Neural Network O.P. Rahib, Amit Kr Yadavb, Hasmat Malika, Abdul Azeemb, Bhupesh Krb, a* a,b
Electrical Engineering Department,National Institute of Technology, Hamirpur 177005,India
Abstract Voltage stability is concerned with the ability of a power system to maintain acceptable voltages at all buses in the system under normal conditions and after being subjected to a disturbance. This paper presents a new technique to determine the static voltage stability of load buses in a power system for a certain operating condition and hence identifies load buses which are close to voltage collapse. A voltage stability index with respect to a load bus is formulated from the voltage equation derived from a two bus network and it is computed using Thevenin equivalent circuit of the power system referred to a load bus. . Buses with values of voltage stability factors close to 1 .0 are identified as the critical buses. And after that, an Artificial Neural Network is developed for voltage stability monitoring. In ANN applications, selection of input variables is an important aspect
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of ICCTSD 2011
Open access under CC BY-NC-ND license.
"Keywords: Voltage stability; Voltage Stability Index; Artificial Neural Network (ANN); Security Assessment;critical bus; Stability Index Prediction"
1. Introduction Voltage stability is a major concern in planning and operations of power systems. It is well known that voltage instability and collapse have led to major system failures; with the development of power markets, more and more electric utilities are facing voltage stability-imposed limits .A system enters a state of voltage instability when a disturbance increases in load demand, or change in system condition causes a progressive and uncontrollable decline in voltage and the process may result in voltage collapse. The main factor causing instability is the inability of the power system to meet the demand for reactive power. Knowledge of the voltage stability margin is of vital importance to utilities in order to operate their system with maximum security and reliability. The system operator must be provided with an accurate and fast method to predict the voltage stability margin so as to initiate the necessary control actions. Several works have been conducted previously for the prediction of voltage stability and proximity to collapse conditions based on conventional techniques, using sensitivity indices and based on continuation methods [1-11]. Continuation method based voltage stability analysis techniques are fairly accurate but hampered by the fact of taking longer computational time being based on repetitive power flow. For online voltage stability, index suits well, if it is accurate indicator of voltage stability margin and can be calculated fast. Some of the works focus on static voltage stability analysis using such instability measuring indicators as that of the popular L-index [6-7]. This index
* Hasmat Malik. Tel.: +91-9736788386; E-mail address:
[email protected]
1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.01.833
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gives sufficiently accurate as well as practical means of the assessment, and can express the stability analysis in simple and operator friendly way. Application of Artificial Neural Network (ANN) to the above-mentioned problem has attained increasing importance mainly due to the efficiency of present day computers. Moreover real-time use of conventional methods in an energy management center can be difficult due to their significant large computational times. One of the main features, which can be attributed to ANN, is its ability to learn nonlinear problem offline with selective training, which can lead to sufficiently accurate online response. ANN approach to voltage stability assessment and improvement has been proposed and various neural network combinations have been used for solving the problem in [12-18]. The ability of ANN to understand and properly classify such a problem of highly non-linear relationship has been established in most of them and the significant consideration is that once trained effectively ANN can classify new data much faster than it would be possible with analytical model. 2. DERIVATION OF VOLTAGE STABILITY INDEX The mathematical formulation for the voltage stability index is derived from voltage equation used in the Improved Distribution load flow technique [19]. The derivation for the voltage stability index is as follows, Consider again a line connecting bus i to i+1,
P i, Qi, V i,
θi Pi+1, Q i+1, V i+1,
θi+1
ri +jxi PLi, QLi
PLi+1, QLi+1
The voltage equation would be:Vi+14+Vi+12[2(Pi+1ri+Qi+1xi)-Vi2] + Pi+12+Qi+12ri2+xi2=0 Where,
P i, Qi =Real & Reactive power injection at bus i V i = Voltage at bus i ri , xi= resistance and reactance of line connecting bus i & i+1
The equation is quadratic inVi+12 and it will have real roots if; Hence from equation (1), 8Pi+1Qi+1rixi - 4Vi2(Pi+1ri + Qi+1xi) + Vi4 – 4(Pi+12xi2 + Qi+12xi2) ≥ 0
(1)
b2-4ac>=0 (2)
This can be simplified to,
4[Vi 2 ( Pi 1ri Qi 1 xi ) ( Pi 1 xi Qi 1ri ) 2 ] 1 Vi 4
(3)
Therefore, the voltage stability index is given by,
L
4[Vi 2 ( Pi 1ri Qi 1 xi ) ( Pi 1 xi Qi 1ri ) 2 ] Vi 4
(4)
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Since,
VV i i 1 cos( VV i i 1 sin(
And,
i i
i 1 i 1
) Vi
2 1
Pi 1ri Qi 1xi
(5)
Pi 1 xi Qi 1ri
)
(6)
Substituting equations (5) and (6) in (4),
L
4[VV i i 1 cos(
i
) Vi Vi 2
i 1
2 1
cos(
i
i 1
)2 ]
(7)
The voltage stability index derived is then applied to the thevenin equivalent circuit looking at the load bus concerned as shown in fig. 2.Vth is the thevenin voltage, which is the open circuit voltage at the bus concerned, ZL φL is the equivalent impedance of the load connected at that bus and Zth is the Thevenin impedance across the bus. The following steps are used to determine the Thevenin’s equivalent circuit with respect to a load bus:a) Run the load flow to obtain the voltage profile of a power system at given loading condition. b) Obtain Vth by running the load flow with the load connected at that bus removed. Applying equation (7) to the Thevenin’s equivalent circuit, gives
L
4[VoVL cos(
o
) VL 2 cos( Vo 2
L
o
L
)2 ]
(8)
L must be kept less than 1.0 to maintain voltage stability. If L exceeds 1.0, according to equation (3) the voltage at the referred bus becomes imaginary which indicates that voltage collapse has occurred in the system. Hence, The Voltage stability index is termed as symbol Land given by equation Voltage Stability Index, Where L= Stability Index, Vo = No load voltage, and VL= Load Voltage
(9)
In order to maintain a stability of voltage condition in the system network, the value of L any load bus must be kept less than 1.0. If the value of L evaluated at load bus approaches 1.0 the voltage is referred as collapse conditions. This index will be used in the voltage stability analysis caused by the heavy loadings. It will be assigned as the target output of the ANN. 3. Proposed ANN Based Approach A multilayer feed forward Artificial Neural Network with error back propagation learning was used. The developed network consists of three basic elements. 1. Neural network Architecture 2. Suitable back propagation learning algorithm 3. Method of training and testing 3.1 Neural Network Architecture The architecture of a developed network consists of input layer, one hidden layer, and one output layer. Sigmoid activation function is used for each neuron. The architecture of develop network is shown in figure3.
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Fig.2. Neural Network Architecture
3.2 Selection of Input Patterns Selection of the training parameters is an important task in designing an ANN. A few important parameters can severely reduce the learn ability of the network. Similarly absence of few important parameters may reduce the accuracy. Total of 300 input/output patterns are generated. Out of 300 patterns, 250 patterns are used for training purpose and 50 patterns are for testing purpose. 28 Inputs are used for IEEE 14-bus system, 25 are bus power injections (active and reactive) and 3 inputs are tap settings of transformers. Numbers of hidden layer neurons are 20 and number of output neurons are 9. 3.3 Training & Testing The training process is performed by using adaptive error back propagation algorithm order to train the developed network with a set of input and targeted output. 250 patterns were randomly selected from the voltage stability results. The network was trained until it achieved a very small MSE typically 0.0022 p.u. The network which was fully trained with the lowest error is capable to be used in the testing process. Performance of Ann to Minimize the RMS Error by showing the training, validation and testing curve is shown in figure5.The generalized capabilities of proposed Neural Network have been investigated by using 50 testing patterns. The reliable network should be able to produce a very good output results. Beside the overall MSE error, the performance of developed neural network can also be justified by using calculating the absolute error for every testing pattern and by using line regression as shown in figure 6.To further identify the accuracy of the developed network, the developed network must be indicating correlation coefficient, R closest to unity (1.0000). Unity value of R indicates zero absolute and RMS error. 4. Results & Discussion Test system presented in this study is the IEEE 14-bus system. Single line diagram of IEEE-14 bus system is shown below:
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1 3
1 4
20
16
19
1 1
1 2 15
17
1 0
18
17
19
6
9
G
G
8
12
10 7
8
11
5
9
4
7 4 5
G
3
6
1 1 2
2
3
G
G
Fig.4. Modified IEEE 14-Bus System
TABLE I VOLTAGE STABILITY INDEX AT DIFFERENT BUSES AT A NORMAL LOADING CONDITION (STABLE CONDITION)
TABLE II. VOLTAGE STABILITY INDEX AT DIFFERENT BUSES WITH 14TH BUS HEAVILY LOADED (UNSTABLE CONDITION)
Bus
Target L
Output L
Error
Bus
4
0.0849
0.0850
0.0001
4
0.2315
0.2314
-0.0001
5
0.0772
0.0774
0.0002
5
0.2115
0.2114
-0.0001
7
0.0944
0.0944
0.0000
7
0.2925
0.2927
0.0002
9
0.1482
0.1481
-0.0001
9
0.4501
0.4508
0.0007
10
0.1465
0.1464
-0.0001
10
0.4032
0.4038
0.0006
11
0.0907
0.0907
0.0000
11
0.2344
0.2345
0.0001
12
0.0654
0.0657
0.0003
12
0.1971
0.1974
0.0003
13 14
0.0985 0.2041
0.0985 0.2035
0.0000 -0.0006
13 14
0.3688 0.9222
0.3691 0.9223
0.0003 0.0001
Target L
Output L
Error
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. 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.
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Fig. 5.Performance of Ann to Minimize the RMS Error
Figure 5 shows the plotting of training, validation and test error to check the progress of training. The training stopped after 15 iterations because the validation error is increased. The result here is reasonable, because the test set error and the validation set error have similar characteristics. TABLE III RESULT OF VOLTAGE STABILITY INDEX PREDICTION USING ANN ON CRITICAL BUS-14 S.N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Output L 0.2035 0.1864 0.1864 0.1991 0.1832 0.1735 0.1611 0.2080 0.1950 0.1694 0.1553 0.1913 0.1603 0.1656 0.2019 0.1348 0.1906 0.1827 0.1927 0.1778 0.1928 0.1772 0.1887 0.1839
BUS 14 Target L 0.2041 0.1865 0.1861 0.199 0.1844 0.1738 0.1616 0.2079 0.1951 0.1694 0.1554 0.1911 0.1602 0.1661 0.2015 0.1339 0.1906 0.1836 0.1918 0.1779 0.1927 0.178 0.1898 0.1839
Error -0.0006 -0.0001 0.0003 0.0001 -0.0012 -0.0003 -0.0005 0.0001 -0.0001 0.0000 -0.0001 0.0002 0.0001 -0.0005 0.0004 0.0009 0.0000 -0.0009 0.0009 -0.0001 0.0001 -0.0008 -0.0011 0.0000
S.N 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Output L 0.1936 0.1906 0.1919 0.1691 0.1919 0.1825 0.1971 0.1450 0.1833 0.1850 0.1621 0.1730 0.1780 0.1698 0.1772 0.1822 0.1895 0.1938 0.1702 0.1840 0.2043 0.2027 0.2001 0.1814
Target L 0.1934 0.1904 0.1922 0.1687 0.1923 0.182 0.1971 0.1452 0.1836 0.1843 0.1626 0.1726 0.1784 0.17 0.1776 0.1826 0.1896 0.1939 0.1701 0.1834 0.2036 0.2013 0.1998 0.1813
Error 0.0002 0.0002 -0.0003 0.0004 -0.0004 0.0005 0.0000 -0.0002 -0.0003 0.0007 -0.0005 0.0004 -0.0004 -0.0002 -0.0004 -0.0004 -0.0001 -0.0001 0.0001 0.0006 0.0007 0.0014 0.0003 0.0001
In table 3, Target output which is voltage stability index through load flow studies and calculated output which is voltage stability index calculated through ANN, is compared and the error is very less. The effect of variation of load on voltage stability index “L” of critical bus is shown in table 4.
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O.P. RahiMalik/ et al. Procedia / ProcediaEngineering Engineering00 30(2011) (2012)000–000 53 – 60 Hasmat TABLE IV RESULT OF VOLTAGE STABILITY INDEX PREDICTION USING ANN ON CRITICAL BUS 14 (WITH HEAVILY LOADED)
S.N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Output L 0.9214 0.8079 0.8289 0.9082 0.8711 0.7185 0.7935 0.8536 0.7545 0.8160 0.9279 0.8332 0.8808 0.8161 0.9024 0.8552 0.9387 0.9307 0.8335 0.7902 0.9429 0.9302
BUS 14 Target L 0.9222 0.8074 0.8291 0.9079 0.8712 0.7186 0.794 0.8553 0.7551 0.816 0.9272 0.8336 0.8812 0.8155 0.9032 0.8552 0.939 0.93 0.8333 0.7908 0.942 0.9297
Error -0.0008 0.0005 -0.0002 0.0003 -0.0001 -0.0001 -0.0005 -0.0017 -0.0006 0.0000 0.0007 -0.0004 -0.0004 0.0006 -0.0008 0.0000 -0.0003 0.0007 0.0002 -0.0006 0.0009 0.0005
S.N 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Output L 0.7817 0.8655 0.8551 0.9192 0.8250 0.9633 0.9526 0.9006 0.8809 0.8072 0.7509 0.7912 0.8326 0.9225 0.9021 0.8945 0.8162 0.8764 0.7128 0.8002 0.7358 0.8794 0.8160
Target L 0.7818 0.8651 0.8558 0.9188 0.8252 0.9649 0.9523 0.9011 0.8814 0.8069 0.7508 0.7916 0.8325 0.9223 0.9019 0.8947 0.8157 0.8762 0.7141 0.8001 0.7361 0.8802 0.8159
Error -0.0001 0.0004 -0.0007 0.0004 -0.0002 -0.0016 0.0003 -0.0005 -0.0005 0.0003 0.0001 -0.0004 0.0001 0.0002 0.0002 -0.0002 0.0005 0.0002 -0.0013 0.0001 -0.0003 -0.0008 0.0001
Fig.7. Accuracy Prediction L- Index on Load Bus 14
5. Conclusion The development of ANN for voltage stability monitoring was presented. The back propagation neural network using MATLAB language has been employed for voltage stability monitoring. From the testing process, it shows that the proposed method is capable in predicting voltage stability index for the load buses in power system network. The proposed method was tested using IEEE-14 bus test system and indicated a good agreement between targeted output and ANN output. Voltage stability index (L-index) has been calculated by conventional method (Newton Raphson;s load flow) and using Artificial Neural Networks. The value of L-index is a measure for voltage stability. The bus with the highest L-index value will be the most vulnerable bus in the system and hence this method helps in identifying the weak areas in the system which need critical reactive power support.
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