Artificial Neural Network Modeling Technique for Voltage Stability Assessment of Radial Distribution Systems

Transcription

1 Minia University From the SelectedWorks of Dr.-Ing. Nasser Hemdan September 6, 2006 Artificial Neural Network Modeling Technique for Voltage Stability Assessment of Radial Distribution Systems Mohamed M. Hamada, Dr., Minia University Mohamed A. A. Wahab, Prof. Dr., Minia University Nasser G. A. Hemdan, Dr. Ing., Minia University Available at:

2 ARTIFICIAL NEURAL NETWORK MODELING TECHNIQUE FOR VOLTAGE STABILITY ASSESSMENT OF RADIAL DISTRIBUTION SYSTEMS Mohamed M. Hamada, Mohamed A. A. Wahab, Nasser G. A. Hemdan Al-Minia University, Egypt ABSTRACT This paper presents an Artificial Neural Network (ANN) based modeling technique for predicting the voltage stability of radial distribution systems. The modeling technique is based on a new voltage stability index for assessment of radial distribution systems Lv. The index is implemented to investigate a 33-bus distribution system. An ANN model which has an input layer with two input vectors (P, Q), one hidden layer, and an output layer, which gives the predicted value for the voltage stability index Lv is suggested to predict the value of this index. The performance of the ANN model is tested by using the results of the 33-bus distribution system. Then the ANN model is checked by two model evaluation indices namely mean absolute percentage error and actual percentage error. Plotting of the simulated results with the ANN output is used to evaluate visually the accuracy of simulation. Extensive testing of the proposed ANN based technique have indicated its viability for voltage stability assessment. INTRODUCTION from voltage collapse. Abd El-Aziz et. al [5] investigated the application of artificial neural networks in voltage stability Distribution systems are distinctly different, in both their assessment using the energy function method. This technique is operation and characteristics from transmission systems. used for calculation of voltage stability margins. El-Keib et. al Modern power distribution systems are constantly being faced [6] used the ANN's for determining the voltage stability with an over-growing load demand. Distribution systems margins based on energy function method. A systematic experience distinct change from a low to high load level every method for selecting the ANN's input variables was developed day. In certain industrial areas, it has been observed that under using sensitivity analysis. Jeyasurya [7] used the ANN's for certain critical loading conditions, the distribution system may evaluation of on-line voltage stability in modern energy control experience voltage collapse [1]. Radial distribution systems centers based on an energy measure, which is an indication of having low reactance to resistance (X/R) ratio causes a the power system's proximity to voltage collapse. Salama et. al considerable IX and IR voltage drops in these systems which [8] applied the ANN's to predict the voltage instability based on may lead them to voltage collapse. Therefore, they are a voltage collapse proximity indicator, which was presented in categorized as ill conditioned systems [2]. [9]. Artificial neural networks provide techniques for solution of This paper suggests an ANN network modeling technique some engineering problems. Their flexible nature allows based on a novel voltage stability index derived and presented representation of many types of data for analysis. Since training in [10,11]. This ANN technique has been implemented to is based on the past as well as existing data of different investigate a 33-bus distribution system. parameters, the results obtained can be more reliable. Also, the computational difficulty is reduced by considerable extent and recent data can be obtained for further analysis [3]. In recent VOLTAGE STABILITY INDEX years, ANN have emerged a promising technology, which has the capability to solve some long-standing power system A new index Lv was derived and implemented for the two busproblems where conventional approaches have difficulty. ANN equivalent model of any N-bus distribution system. This index has already been applied to some power system problems such is defined as [10, 1]: as security assessment, real time control of capacitors, protection, and load forecasting. ANN has also been applied to the voltage stability assessment problem [4]. [4S2Cos (0 + (p)] (1) Y22 [V1Cos (6)]2 El-Kady et. al [4] introduced an ANN based technique for prediction of voltage stability in electrical power systems. Selection of input variables for training ANN is obtained using a performance index, which reflects the proximity of system 1011

3 Where VI: Voltage at bus No. 1, and its angle is 6, S2: Load apparent power, and its angle is (p, Y22: Sum of admittances connected to and its angle is 0. bus No. 2, i/p 1 w(l I Lv is a stability index that indicates the status of the system and shows how close the operating point to the point of collapse. i/p2 When the value of the index equals to zero that means there is no load, and between zero and one the system operates in the Output [G] stable region and the values greater than one mean that the Mupu[/ system is unstable. ANN ASSESSMENT OF VOLTAGE STABILITY BASED ON Lv INDEX A multi-layer feed forward artificial neural network with back- p [nxr] Hiddenlayer propagation learning is proposed for the prediction of the Lv voltage stability index which reflects the proximity of the Figure 1 A schematic diagram of a multilayer feed forward distribution system to voltage collapse. The ANN based neural network structure technique maps the relationship between the load total active and reactive powers of the distribution system and the voltage stability index Lv according to the present load pattern. A GENERATION OF TRAINING SET SAMPLES neural network model depends on the variables used for predicting the Lv index. The Lv index is obtained on each bus A 33-bus [12] distribution system is employed in this study. by using certain reconfiguration of the distribution system Instead of choosing all buses to be studied with the proposed [10,11]. Therefore, it is obvious to model the data of technique it is better to choose the weakest buses that affect the reconfigurated system by a certain neural network pattern. This voltage stability of the 33-bus distribution system. By technique helps to study the effect of the load at each bus on computing the value of the index found in [1] at all buses of the voltage stability index. Its implementation is effective 33-bus system. It is found that the area containing buses 13, 14, especially when the load variation can be monitored at each bus or at a certain bus. DESIGN OF ANN MODEL i/p n w(n, 15, 16, 17, and 18 is the weakest area. A gradual increase of the active power load at these buses by a step of 10 kw at the same power factor of the base load is implemented. Then the value of the Lv index is computed for each bus. The topology of a multi-layer feed-forward ANN consists of an EVALUATION OF MODELING TECHNIQUE input layer, one or several hidden layers and an output layer. The proposed multi-layer neural network structure is shown in Two model evaluation indices have been implemented. They Figure 1. As seen in Eq. 1 the value of Lv index depends on are mean absolute percentage error (MAPE) [13,14] and actual many factors but the most effective factor is the total load percentage error (APE) [15]. These indices have been apparent power (active and reactive power). Therefore the load computed for predicted values. They are defined as follows: total active and reactive powers govern the voltage stability of a radial distribution system. Thus they are chosen as inputs to { Y - Y laxi 00/y } the ANN. The number of input nodes "n" is two for total active MAPE ac pr ac (2) and reactive powers. The number of neurons in the hidden layer N depends on the number of training vectors and the number of (y - Y ) unknown weights and biases to be evaluated. The number of APE ac pr 0 (3) output layer neuron is one, which is the voltage stability index Yac Lv. The input of training patterns has a size of 2 x R where "R" is the number of data used for training. The value of R has been Yac: The actual value of voltage stability index varied at each bus under study. The output "G" is the voltage stability index L. The training process has been carried out Ypr The predicted value of the index and using back-propagation learning algorithm. N : The total number of values predicted and also the limit of the summation process. Low values of MAPE satisfy the statistical evaluation of prediction validity [15]. A pre-specified acceptable error is justified by APE. where, 1012

4 TRAINING AND TESTING OF ANN MODELS and validity of the proposed ANN model. The proposed ANN model can be used for the assessment of voltage stability based Neural network model is trained by applying the supervised on Lv index. learning procedure. The Neural Network Toolbox in MATLAB [16] is used to implement the proposed ANN technique. Each Table 1 Data used for training and prediction of the input vector and the corresponding voltage stability index Lv proposed ANN model at the weakest buses of the 33-bus are used to train the ANN model. During training the weights system (step of PL is 10 kw for constant power factor) and biases are iteratively adjusted to minimize the network Bus No. From To performance function [16]. The trained network is used to predict the value of the Lv index for new input vectors, which PL) QL) PL) QL) were not used for training the ANN models, and ANN results total total total total compared with the simulation results obtained for these new (kw) (kvar) (kw) (kvar) input vectors. The network is retrained if the global error is not within the specified limit. Once the network is satisfactory trained it is ready for use in the prediction mode. Table illustrates the values of the total active and reactive power loads used for training and predicting procedures RESULTS AND DISCUSSION A. Voltage Stability Index Lv Figures from 2 to 7 show the predicted and simulated values of voltage stability index Lv where the load increases at the weakest buses No. 13, 14, 15, 16, 17 and 18 respectively. The Bus No. From To values shown in the figures are the simulated and predicted PL) QL) PL) QL) values. The prediction of Lv index is carried out for total active and reactive power up to the critical values while the load total total total total increases at a certain bus. These critical values are the limit (kw) (kvar) (kw) (kvar) values after which the voltage collapse will occur. Table 2 illustrates the number of training pair's vectors, number of testing vectors, and the figure number at which results are t presented. Figures from 2 to7 show the output of the proposed ANN model for each bus and the simulated values of the Lv Index The ANN outputs and simulated values of Lv index are plotted against the total apparent power load of the distribution system for each bus. It can be observed that the output of the ANN (predicted values of Lv) for each bus is coincident with the simulated values of the Lv index. Table 2. Training and testing pair's vectors at each bus B. Actual Percentage Error (APE) Bus No. of No. of % of Results in To evaluate the accuracy of predicted values, the actual percentage errors at the weakest buses have been calculated. No. training testing load Fig. The values of APE for the predicted values with the loads vectors. vectors. increase increase at buses No. 13, 14, 15, 16, 17 and 18 are given in Figure 8. From Figure 8 it can be seen that the APE varies over a very limited range less than ± 0.5%, which can be considered as indication of validity of the proposed ANN model C. Mean Absolute Percentage Error (MAPE) Figure 9 shows the mean absolute percentage error MAPE for the predicted values while the loads increase at buses No. 13, 14, 15, 16, 17 and 18. Figure 9 shows small values of MAPE These values approximately zero. Small values of MAPE indicate good prediction from the view point of statistical evaluation of the model. A summary of maximum and minimum actual percentage errors and mean absolute percentage errors at the weakest buses of the 33-bus system are illustrated in Table 3. From Table 3 it can be seen that the results obtained for MAPE and APE justify the applicability 1013

5 I.ivlP Iirillair RGSUIS) Index lulrnlresixluss Lvkidex{ANN~~~~~~~~~~~~~~~~~~~~~~~~Lv141 AN J aj : %.- %.* * ,, >M > 0 0 Total Apparent Power (R.U.) Total Appaent Power(P.U}) 1) Figure 2 Simulated and predicted values of the Lv index. Figure 5 Simulated and predicted values of the Lv index. (With the load increase at bus No.13) (With the load increase at bus No. 16) > I.> 0m 16 _ W* q - : < _ f,0 gf~~~~~~~~~~~~~~~~~~~~~~~~~~a X SXf vf.~~~~~~~~~~sm ttl 4/.f,Q-gQP~~A LV iode ISIMUIamio Nsd LV Index {SWImul*o resutsil UIndex (ANNj Ly IndexANi i2~~~ ~ ~ ~~~~~~~~~~~~~~ 5 -F; S f fs T,9-2 % i S? Ss ToltaI Appa rent Po e (P.U) Total Active Poer (P.U.) Figure 3 Simulated and predicted values of the Lv index. Figure 6 Simulated and predicted values of the Lv index. o (With the load increase at bus No. 14) 0 (With the load increase at bus No. 17) X G9 >~~pl > L_ Er_ s0' 0~~~~~11 e, if~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- : > fff f / R >" ff ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ t 8 _~~~~~~~~s 0~~~~~~~~~~~~~11

6 0 w * K [JJ 3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.5 hlthe load increse twbs 18. x R 4 _ * wh~~~~~~~~~~~~~~~~~~~~il. the goad increse twbs 143 Cq 0.2 mi h. *. - s tws. o~~~~~~~~~~~~~~o 3.5. v*. * D~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i' th I..d -.s. tw _7.U vs x v 02 whi the oad increase atbus 13Q -0. 1I 2 whil tthe load increase -0.3 whiletheloadincreaseatbus16 attbus17 while he load increase a bus ujr C atbus 15 *l Total Apparent Power (P.U.) Total Apparent Power (P.U.) Figure 8 APE for the predicted values of Lv index. (With Figure 9 MAPE for the predicted values of Lv iudex. (With the load increase at buses No. 13, 14, 15, 16, 17 and 18) the load iucrease at buses No 13, 14, 15, 16, l7aud 18) _* CONCLUSIONS 7. Jeyasurya-B, "Artificial Neural Networks for Power System The contribution of this paper is the application of the artificial Steady State Voltage Instability Evaluation," Electric Power neural networks for the prediction of the inception of voltage Systems Research, Vol. 29, No. 2, PP , instability in radial distribution systems. An ANN model has been trie an imlmne fo th prdcto oftevotg 8. M. M. Salama, E. M. Saied, M. M. Abou-Elsaad and E.F. Ghariany, "Estimating the Voltage Collapse Proximity stability index Lv and the results show that: ANN structure of an input layer with two input vectors (P, Q), one hidden layer, Indicator Using Artificial Neural Network," Energy Conversion M and an output layer, which gives the predicted value for the & Management, Vol. 42,PP , voltage stability index Lv, has proved to be reliable. Two model 9. P. Kessel and H. Glavitsch, "Estimating the Voltage Stability evaluation indices (APE and MAPE) were implemented to of a Power System," IEEE, Trans. on Power Delivery, Vol. justify the validity and applicability of the proposed ANN PWRD- 1, No. 3, PP , July models. 10. M. M. Hamada, M. A. A. Wahab and N. G. Hemdan, "A REFERENCES New Criterion for Assessing Voltage Stability in Radial Distribution Systems," Proc. MEPCON, Tenth International 1. M. Charkravorty and D. Das, "Voltage Stability Analysis of Middle East Power System Conference, Portsaid, Egypt, Vol. Radial Distribution Networks," Electrical Power & Energy 2, PP , Dec , Systems, Vol. 23, PP , N. G. A. Hemdan, "A study on the Phenomenon of Voltage 2. M. Moghavvemi and M. 0. Faruque, "Technique for Instability in Electric Power Systems," M.Sc Thesis, Minia Assessment of Voltage Stability in Ill-Conditioned Radial University, Minia, Egypt, Distribution Network," IEEE Power Engineering Review, PP , January M. E. Baran and F. F. Wu, "Network Reconfiguration in Distribution Systems for Loss reduction and Load Balancing," 3. K. M. Sharma and P. N. Sreedhar, "Intelligent Approach for IEEE Trans. on Power Delivery, Vol. 4, No. 2, PP , Efficient Operation of Electrical Distribution Automation April Systems," Proc. TENCON, the conference on Convergent Technologies for the Asia-Pacific, Bangalore-India, Vol. 2, PP. 13. L. M. Saini, and M. K. Soni, "Artificial Neural Network , October 15-17, Based Peak Load Forecasting Using Conjugate Gradient Methods," IEEE Trans. on Power System, Vol. 17, No. 3, PP. 4. F. M. El-Kady and A.Y. Abd El-Aziz, "Voltage Stability , Assessment of Electrical Power System Using Artificial Neural Networks," Journal of Engineering and Applied Science, 14. T. Senjyti, H. Takara, K. Uezato and T. Funabashi, "One- Faculty of Engineering, Cairo University, Vol. 48, No. 4, PP. Hour-Ahead Load Forecasting Using Neural Network," IEEE , August Trans. on Power Systems, Vol. 17, No. 1, PP , A. Y. Abd El-Aziz, M. M. Abu El-Naga, K. M. El-Bahrawy 15. M. A. A. Wahab, "Artificial Neural Network-Based and M. A. El-Sharkawy, "ANN-Based Technique for Prediction Technique for Transformer Oil Breakdown Predicting Voltage Collapse in Power Systems," Proc. Voltage," Electric Power Systems Research, Vol. 71, PP. 73- MEPCON, Ninth International Middle East Power Conference, 84, Minoufiya, Egypt, PP. 9-15, January A. El-Keib and X. Ma, "Application of artificial neural networks in voltage stability assessment," IEEE, Trans. on Power Systems, vol.10, no. 4, pp , November Neural Network Toolbox for Use with MATLAB (6), User Guide Version 1015