ANN BASED ONLINE ESTIMATION OF
VOLTAGE COLLAPSE PROXIMITY
INDICATOR
G. BALAMURUGAN
Lecturer in Electrical Engineering,
Annamalai University, Annamalainagar-608002, Tamil Nadu, India [email protected]
P. ARAVINDHABABU
Professor of Electrical Engineering,
Annamalai University, Annamalainagar-608002, Tamil Nadu, India [email protected]
Abstract :
Voltage stability has recently become a challenging issue in many power systems. There are different methods used to study the voltage collapse phenomenon but most of them take significant computation time and are not suitable for on-line applications. Fast voltage stability assessment tools are required in order to ensure the secure operation of the present day power systems, as voltage collapse can occur quite abruptly in systems. Therefore a new ANN based on-line approach that requires minimum input for estimation of voltage collapse proximity indicator for each critical bus under normal and contingent conditions is developed in this paper. Test results on IEEE-14 bus system are presented to show its computational accuracy.
Keywords: artificial neural network; voltage stability; voltage collapse proximity indicator.
1. Introduction
Progressive energy demands and depletion of the existing generation and transmission resources due to various economic, environmental and regulatory changes have evolved a new type of problem, referred to as voltage instability or voltage collapse in power systems. Voltage collapse is generally triggered by large disturbances such as loss of generation, transmission lines or transformers and characterized by a slow variation in system operating point due to the inability of the network to meet the increasing demand for reactive power in such a way that the voltage magnitude gradually decreases until a sharp accelerated change occurs. Many utilities around the world have experienced major blackouts caused by voltage instabilities [1-2].
Voltage stability has become an increasingly important phenomenon in the operation and planning of the present day power systems. A number of methods for voltage stability analysis have been suggested such as P-V curves, V-Q curves, continuation power flow etc [2]. In addition, a number of voltage stability indices such as voltage collapse proximity indicator (VCPI) [3-6], the minimum singular value of power flow jacobian matrix [7], the loading margin [8] and the fuzzy based approach [9] have been proposed in the literature to estimate the proximity of the power system to voltage collapse. However, most of these methods involve a rigorous procedure and hence are suitable only for off-line studies.
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.
A new ANN based method that requires only four inputs, irrespective of the system size, for estimation of VCPI for each chosen bus under normal and/or under contingent conditions is proposed in this paper. This approach provides the voltage stability margin after learning the inherent mapping between the power system operating conditions and its voltage stability margin. The proposed technique is tested on IEEE-14 bus test system and the results are tabulated to demonstrate its computational accuracy.
2. VCPI
Selection of a suitable voltage stability assessment method is the first step towards developing an online VCPI estimation scheme. The VCPI, also called L indicator that varies in the range between 0 and 1 for each load bus, introduced by Kessel and Glavitch [3], is used in this work. This indicator involves a solved power flow, from where variables and parameters are acquired to compute the indicator for voltage stability. The L-indicator for any load bus-j is defined by
j G i
i ji j
V V F
L
1 jL (1)
Where L
= set of load buses G
= set of generator buses Vj = complex voltage at load bus-j
Vi = complex voltage at generator bus-i
ji ji ji F
F = elements of hybrid-F matrix The F is computed using
F YLL YLG1
(2)
where [YLL] and [YLG] are sub-matrices of the Y-bus matrix.
The global indicator LGdescribing the stability of the complete system is given by
jL j G L
L
max
(3)
The maximum value of this indicator, close to one, is indicative of the proximity to power flow divergence, which is prone to voltage collapse. The minimum value, close to zero, is indicative of the most stable state. The bus with the highest L-index will be the most vulnerable bus, which reflects the global stability, in the system. 3. Proposed Method for Estimation of VCPI
The versatile nature of ANNs have made them popular for pattern mapping or function approximation and frequently preferred for solving complex power system problems. A multi-layer feed forward network, seen in Fig. 1, consisting of an input layer, an output layer and a hidden layer with each comprising of a set of neurons and trained by backpropagation algorithm is used in this approach [17].
3.1. Selection of Input Variables
There are a large number of input data such as real and reactive power injection at each bus, bus voltages, etc related to the VCPI in a typical power system, and it would be very time consuming to train a neural network with all the input data, as the number of connection weights and neurons would be extremely large. It is thus essential to reduce the number of inputs to a neural network and select an optimum number of mutually independent inputs, which are able to clearly establish the input-output relationship.
The following four input variables, irrespective of the system size, are heuristically chosen for the ANN model of the vulnerable bus k.
k
L
P , the real power demand at the interested vulnerable bus k,
k
L
Q , the reactive power demand at the interested vulnerable bus k,
PNET, the system net real power demand,
QNET, the system net reactive power demand,
3.2. Contingency Analysis
The standard procedure in most utilities is to examine the effects of all possible outages, one at a time. It will be time consuming, if all single outages are analyzed for large power systems. Therefore a selected number of worst-case contingencies, called credible contingencies, are considered in developing the proposed model. 3.3.Number of Output Variables
If there are
n
-credible contingencies, the network then contains one output for normal network conditions andn
-output forn
-credible contingencies, resulting in n1 output variables as
k
n k k k k
o L L L L
L , 1 , 2 , 3 ...., (4) where Lok represents VCPI value for k
th
bus under normal network conditions X1
X2
X3
H1
H2
H3
H4
Y1
Y2
Input layer Hidden layer Output layer
Fig. 1. Architecture of feed forward neural network
A N N m o d el for b u s-k
PLk
QLk
PN E T
QN E T
Lok
L1k
L2 k
Lnk
k j
L
represents VCPI value for kth bus under jth line/generator outage conditions3.4. Generation of training and testing data
Training data is the only available information to build the ANN model and so they must represent the complete possible operating conditions of the system. The testing data is used to assess the training performance and avoid the over training problem. The input-target patterns are generated using the following procedure for each of the vulnerable bus k.
A range of load patterns are first generated by randomly perturbing the load from the reasonable lower expected loading level to the point of voltage instability. Initially one variable preferably PLk is chosen and set at a lower loading level while the remaining three are perturbed in small steps one by one in order to cover the entire data range. Then PLk is incremented and the remaining three are again
adjusted. This process is repeated till PLk reaches the maximum loading level. Then the second variableQLk is chosen and the remaining three variables are adjusted accordingly. The values of
NET
P and QNET are distributed to all load buses other than bus k in proportion to their base case
values in order to obtain widely varying combinations of load patterns with different power factors.
The VCPI at bus k is computed after carrying out the pre-contingency load flow for each load pattern and then the single line/generator outage specified in the credible contingency list are simulated one by one. The corresponding VCPI values at bus k are computed for forming the training/testing data set as follows.
k
n k k k k o NET NET k L k
L Q P Q L L L L L
P , , , , 1 , 2 , 3 ...., (5)
The generated input-target data are split into two partitions: the first is the training data, which is used to train the network and the second is the testing data, which is used to assess how well the network is generalised. There is a possibility of obtaining good performance on the training data followed by much poor performance on the test data. This can be avoided by ensuring that the training data is uniformly distributed.
3.5. Data normalization
During training of the neural network, higher valued input variables may tend to suppress the influence of smaller ones. Besides, if the raw data is directly applied to the network, there is a risk of the simulated neurons reaching the saturated states. If the neuron becomes saturated, then the changes in the output value will produce a very small change or no change in the output value. This affects the network training to a great extent. The raw data is therefore normalised before it is applied to the neural network. One way to normalise the data
x
is by using the expression:
R R R
n L
x x
L U x x
x
min max
min (6)
where xnis the normalised value
min
x and xmaxare the minimum and maximum values of the variable x respectively
R
L and UR lower and upper range for normalisation respectively
3.6. Training and testing
4. Simulation Results
The proposed approach (PA) is tested on IEEE 14 bus system. Initially the fast-decoupled load flow followed by VCPI computations for all load buses are carried out for the base-case load demands. Bus-14, whose VCPI is the largest, is identified as the most vulnerable bus. A list of credible contingencies that includes an outage of a line in between bus 4 and bus 13 and outage of a generator at bus-2, are chosen to design the neural network. There are thus four inputs and three outputs for the proposed ANN model to estimate VCPIs for the critical bus 14.
The input-target database for both training and testing data is generated by perturbing the real and reactive power demands at bus 14 as well as the net power demand of the system as described in section 3.4. The data are normalised and thereafter the ANN with four input neurons and three output neurons is trained many times with different combinations of hidden layers and hidden neurons. Repeated trial and error studies with training and testing data show that two hidden layers, each with five hidden neurons, are quite satisfactory for the proposed ANN model for estimation of VCPIs.
The network is then tested using projected input data that corresponds to different loading patterns and the results are compared with that of the of the conventional approach (CA), which was earlier used to generate the database, in Table-1. The analysis of this table clearly reveals that the proposed approach quickly provides VCPI values for bus 14 with reasonable accuracy under normal and contingent conditions in the credible outage list for the projected load pattern. Lo14 not only the indicates the local voltage stability of bus 14 but also
indicates the global voltage stability. In a similar fashion, a number of models can be developed for each of the vulnerable bus. It should be noted that when the VCPI exceeds the threshold value, the system enters the region of voltage instability. The threshold value, chosen as 0.2 in this study, is based on the system configuration and the operating state.
It is also observed from Table 1 that the operating point is in the unstable region for test case-5 and requires immediate corrective actions such as reactive power compensation, load curtailment, etc. to bring the system to a safe operating region. However, the system is in the safe region for the first four test cases but it may enter the region of voltage instability for test cases 1 and 4 on the occurrence of outage-1.
Table –1 Comparison of Results obtained by proposed approach with conventional approach
Test Case
Input ( all quantities in per unit)
Method
Output / VCPI
14
L
P QL14 PNET QNET L014
14 1
L L214
1 0.1300 0.0700 2.7000 1.6000 CA PA
0.1224 0.1228
0.2039 0.2034
0.1339 0.1347 2 0.1500 0.0900 1.8000 1.3500 CA
PA
0.0911 0.0914
0.1408 0.1409
0.0941 0.0947 3 0.1800 0.0800 2.1000 1.0100 CA
PA
0.0893 0.0897
0.1359 0.1354
0.0904 0.0918 4 0.2200 0.1300 2.1000 1.5800 CA
PA
0.1327 0.1329
0.2102 0.2100
0.1442 0.1440 5 0.3500 0.1750 3.6000 1.2000 CA
PA
0.2360 0.2360
0.4381 0.4381
0.2685 0.2685
The effect on voltage stability of the system for a projected change in load pattern from the current operating point may be studied by changing the input values as
NET NET NET NET
k L k L k L k
L P Q Q P P Q Q
P , , , and presenting them to the neural network. Table-2 presents the VCPI values for change in load patterns, treating test case-3 of Table-1 as the current operating point. It is very clear that the VCPI values increase with load demand and the operator can take decisions based on the obtained VCPI values. It is observed that the proposed ANN model is ideally suitable for estimation of VCPI values of vulnerable buses without considering the entire power system or without using any rigorous iterative calculations, which will help the operator for foreseeing the system behaviour from stability point of view for projected load patterns.
Preventive measures similar to switching of capacitor banks must be taken in the event of system entering the unstable region. The enhancement of voltage stability under critical conditions may be studied by providing VAR support in steps at local bus-k or at buses other than the local bus-k by changing the input values as
NET NET NET
k L k L k
L Q Q P Q Q
bus-14. It is very clear from these results that either 0.03 per unit of VAR at bus-14 or 0.09 per unit of VAR at other buses will keep the system in a secure condition, even if outage-1 occurs. It is observed that the proposed ANN model is ideally suitable for estimation of VCPI values of vulnerable buses without considering the entire power system or without using any rigorous iterative calculations, which will help the operator for foreseeing the system behaviour from stability point of view for projected load patterns and also provides approximate amount of VAR compensation required to retain the system in the stable region.
Table 2 Effect on voltage stability for projected load changes
Current operating point (Test case-3 of Table-1)
01 . 1 10 . 2 08 . 0 18 . 0 14 14 NET NET L L Q P Q P Sl. No.
Projected Change in Load Demand Expected values of VCPI
14 L P 14 L Q
PNET QNET L014 L114 L214
1 --- --- --- --- 0.0897 0.1354 0.0918
2 0.02 0.01 0.02 0.01 0.0954 0.1438 0.0978 3 0.04 0.02 0.04 0.02 0.1014 0.1527 0.1042
4 0.10 0.05 0.10 0.05 0.1209 0.1820 0.1259
5 0.17 0.10 0.17 0.10 0.1511 0.2282 0.1577
6 --- --- 0.90 0.45 0.1404 0.2326 0.1544
7 --- --- 1.40 0.70 0.2570 0.5168 0.2685
8 --- --- 1.90 0.95 0.9998 1.0000 1.0001
Table 3 Effect on voltage stability for VAR compensation
Current operating point (Test case-4 of Table-1)
58 . 1 10 . 2 13 . 0 22 . 0 14 14 NET NET L L Q P Q P
Location of VAR support
Change in Input Data Expected values of VCPI
14
L
Q
QNET 14
0
L L114
14 2
L
No VAR support --- --- 0.1329 0.2100 0.1440
VAR support only at bus-14
0.015 0.015 0.1284 0.2029 0.1387 0.030 0.030 0.1242 0.1961 0.1336 0.045 0.045 0.1203 0.1897 0.1289 Net VAR support in
the system other than bus-14
--- 0.030 0.1309 0.2062 0.1414
--- 0.060 0.1290 0.2025 0.1389
--- 0.090 0.1272 0.1990 0.1364
--- 0.120 0.1254 0.1956 0.1341
5. Conclusion
Acknowledgments
The authors gratefully acknowledge the authorities of Annamalai University for the facilities offered to carry out this work.
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