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 radialdistribution systems. The modeling technique is based on a new voltage stability index for assessment of radial distribution systemsLv. The index is implemented to investigate a 33-bus distribution system. An ANN model which has an input layer with two inputvectors (P, Q), one hidden layer, and an output layer, which gives the predicted value for the voltage stability index Lv is suggested topredict 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 theproposed ANN based technique have indicated its viability for voltage stability assessment.

INTRODUCTION from voltage collapse. Abd El-Aziz et. al [5] investigated theapplication of artificial neural networks in voltage stability

Distribution systems are distinctly different, in both their assessment using the energy function method. This technique isoperation and characteristics from transmission systems. used for calculation of voltage stability margins. El-Keib et. alModern power distribution systems are constantly being faced [6] used the ANN's for determining the voltage stabilitywith an over-growing load demand. Distribution systems margins based on energy function method. A systematicexperience distinct change from a low to high load level every method for selecting the ANN's input variables was developedday. In certain industrial areas, it has been observed that under using sensitivity analysis. Jeyasurya [7] used the ANN's forcertain critical loading conditions, the distribution system may evaluation of on-line voltage stability in modern energy controlexperience voltage collapse [1]. Radial distribution systems centers based on an energy measure, which is an indication ofhaving low reactance to resistance (X/R) ratio causes a the power system's proximity to voltage collapse. Salama et. alconsiderable IX and IR voltage drops in these systems which [8] applied the ANN's to predict the voltage instability based onmay lead them to voltage collapse. Therefore, they are a voltage collapse proximity indicator, which was presented incategorized as ill conditioned systems [2]. [9].

Artificial neural networks provide techniques for solution of This paper suggests an ANN network modeling techniquesome engineering problems. Their flexible nature allows based on a novel voltage stability index derived and presentedrepresentation of many types of data for analysis. Since training in [10,11]. This ANN technique has been implemented tois 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, thecomputational difficulty is reduced by considerable extent andrecent data can be obtained for further analysis [3]. In recent VOLTAGE STABILITY INDEXyears, ANN have emerged a promising technology, which hasthe capability to solve some long-standing power system A new index Lv was derived and implemented for the two bus-problems where conventional approaches have difficulty. ANN equivalent model of any N-bus distribution system. This indexhas 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 tothe voltage stability assessment problem [4]. [4S2Cos (0 + (p)] (1)

Y22 [V1Cos (6)]2El-Kady et. al [4] introduced an ANN based technique forprediction of voltage stability in electrical power systems.Selection of input variables for training ANN is obtained usinga performance index, which reflects the proximity of system

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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 bus No. 2, i/p 1 w(l Iand its angle is 0.

Lv is a stability index that indicates the status of the system andshows how close the operating point to the point of collapse. i/p2When the value of the index equals to zero that means there isno 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.

i/pnANN ASSESSMENT OF VOLTAGE STABILITY BASED w(n,

ON Lv INDEX

A multi-layer feed forward artificial neural network with back- p [nxR] Hiddenlayerpropagation learning is proposed for the prediction of the Lvvoltage stability index which reflects the proximity of the Figure 1 A schematic diagram of a multilayer feed forwarddistribution system to voltage collapse. The ANN based neural network structuretechnique maps the relationship between the load total activeand reactive powers of the distribution system and the voltagestability index Lv according to the present load pattern. A GENERATION OF TRAINING SET SAMPLESneural network model depends on the variables used forpredicting 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 thereconfigurated system by a certain neural network pattern. This voltage stability of the 33-bus distribution system. Bytechnique 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 thevoltage 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 15, 16, 17, and 18 is the weakest area. A gradual increase of theor at a certain bus. 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 ofthe Lv index is computed for each bus.

DESIGN OF ANN MODEL

The topology of a multi-layer feed-forward ANN consists of an EVALUATION OF MODELING TECHNIQUEinput 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. TheyFigure 1. As seen in Eq. 1 the value of Lv index depends on are mean absolute percentage error (MAPE) [13,14] and actualmany factors but the most effective factor is the total load percentage error (APE) [15]. These indices have beenapparent 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 ofa 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 Ndepends 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 YacLv. The input of training patterns has a size of 2 x R where "R" where,is the number of data used for training. The value ofR has been Yac: The actual value ofvoltage stability indexvaried at each bus under study. The output "G" is the voltagestability index L . The training process has been carried out Ypr The predicted value of the index andusing 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 ofprediction validity [15]. A pre-specified acceptable error isjustified by APE.

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TRAINING AND TESTING OF ANN MODELS and validity of the proposed ANN model. The proposed ANNmodel 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 theinput vector and the corresponding voltage stability index Lv proposed ANN model at the weakest buses of the 33-busare 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 Toperformance function [16]. The trained network is used topredict 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 totalcompared with the simulation results obtained for these new (kW) (kVAr) (kW) (kVAr)input vectors. The network is retrained if the global error is notwithin the specified limit. Once the network is satisfactory 9 13 3715 2290.01 4505 2750.84trained it is ready for use in the prediction mode. Table 1 14 3715 2290.01 4455 2783.34illustrates the values of the total active and reactive powerloads used for training and predicting procedures. 15 3715 2290.01 4715 2456.68

RESULTS AND DISCUSSION 16 3715 2290.01 4525 2560.00

A. Voltage Stability Index Lv 17 3715 2290.01 4245 2565.00Figures from 2 to 7 show the predicted and simulated values of 18 3715 2290.01 4205 2507.00voltage stability index Lv where the load increases at theweakest buses No. 13, 14, 15, 16, 17 and 18 respectively. The Bus No. From Tovalues shown in the figures are the simulated and predicted PL) QL) PL) QL)values. The prediction of Lv index is carried out for total activeand reactive power up to the critical values while the load total total total totalincreases at a certain bus. These critical values are the limit (kW) (kVAr) (kW) (kVAr)values after which the voltage collapse will occur. Table 2illustrates the number of training pair's vectors, number of 13 4515 2756.67 5399 3272.00testing vectors, and the figure number at which results are t 14 4465 2790.01 5199 3279.34presented. Figures from 2 to7 show the output of the proposed 15 4725 2458.34 5464 2581.51ANN model for each bus and the simulated values of the LvIndex The ANN outputs and simulated values of Lv index are 16 4535 2563.35 5223 2792.69plotted against the total apparent power load of the distribution 17 4255 2570.59 4933 2898.96system for each bus. It can be observed that the output of theANN (predicted values of Lv) for each bus is coincident with 18 4215 2512.23 4894 2814.01the simulated values of the Lv index.

Table 2. Training and testing pair's vectors at each busB. Actual Percentage Error (APE) Bus No. of No. of % of Results inTo evaluate the accuracy of predicted values, the actualpercentage 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. increaseincrease at buses No. 13, 14, 15, 16, 17 and 18 are given inFigure 8. From Figure 8 it can be seen that the APE varies over 13 80 89 19.8 2a very limited range less than ± 0.5%, which can be 14 75 75 16.7 3considered as indication of validity of the proposed ANNmodel. 15 100 75 15.9 4

16 82 70 15.4 5C. Mean Absolute Percentage Error (MAPE)Figure 9 shows the mean absolute percentage error MAPE for 17 61 61 16.2 6the predicted values while the loads increase at buses No. 13,14, 15, 16, 17 and 18. Figure 9 shows small values of MAPE. 18 50 69 16.4 7These values approximately zero. Small values of MAPEindicate good prediction from the view point of statisticalevaluation of the model. A summary of maximum andminimum actual percentage errors and mean absolutepercentage errors at the weakest buses of the 33-bus system areillustrated in Table 3. From Table 3 it can be seen that theresults obtained for MAPE and APE justify the applicability

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Total Apparent Power (R.U.) Total Appaent Power(P.U})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)

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Figure 8 APE for the predicted values of Lv index. (With Figure 9 MAPE for the predicted values of Lv iudex. (Withthe 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 SystemThe contribution of this paper is the application of the artificial Steady State Voltage Instability Evaluation," Electric Powerneural networks for the prediction of the inception of voltage Systems Research, Vol. 29, No. 2, PP. 85-90, 1994.instability in radial distribution systems. An ANN model has

trie an imlmne fo th prdcto oftevotg 8. M. M. Salama, E. M. Saied, M. M. Abou-Elsaad and E.F.been Ghariany, "Estimating the Voltage Collapse Proximitystability index Lv and the results show that: ANN structure ofIndicator Using Artificial Neural Network," Energy Conversionan input layer with two input vectors (P, Q), one hidden layer,M

and an output layer, which gives the predicted value for the & Management, Vol. 42,PP. 69-79, 2001.voltage stability index Lv, has proved to be reliable. Two model 9. P. Kessel and H. Glavitsch, "Estimating the Voltage Stabilityevaluation 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. 346-354, July 1986.models.

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