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Application of artificial neural network for analysis of self-excited induction generator.

ABSTRACT

It is observed that conventional techniques to analyse the steady state analysis of Self-Excited Induction Generator (SEIG) involve cumbersome mathematical procedures. In this paper an Artificial Intelligence (AI) technique has been used to analyse the behaviour of Self-Excited Induction Generator, which does not require rigorous modelling as required in conventional techniques. Proposed Artificial Neural Network (ANN) model has been implemented to predict the effect of speed, capacitance and load on generated voltage and frequency of SEIG. Experimental data is used for the training of ANN. Results obtained from the trained ANN are found to be in close agreement with the experimental results.

Keywords: Self-Excited Induction Generator, Artificial Neural Networks.

1. INTRODUCTION

Among renewable energy sources, wind energy conversion scheme is most promising and cost effective. Due to zero fuel cost and environmentally clean, electric power generation from wind farms is increasing in an amazing way. Wind powered systems have been widely used since tenth century for water pumping, grinding grains and other low power applications. In 1931, the Russians built a large windmill with a 100 ft diameter blade, but it had very low conversion efficiency [1].

Due to number of advantages of induction generators such as simple & rugged construction, low cost, absence of DC exciter etc., these have been found most suitable for wind energy conversion schemes. Induction generators can operate in two modes i.e. Grid Connected Operation and Isolated Induction Generator Operation. Grid connected operation is feasible when normal AC supply grid is available near the site. Induction machine connected to the grid operates as externally excited induction generator, while taking the excitation current from the grid, for which the operating speed of the machine must be greater than the synchronous speed. The output voltage and frequency does not change with loading conditions but active power generated by the machine is a function of slip. Induction machine connected across the capacitor bank when driven by the prime mover within the limits of lower and higher cut-off speeds operates as self excited induction generator. Under these conditions the capacitor bank meets the total reactive power requirements of the machine and load. Active power generated by the rotor is delivered to the load through stator.

This concept of self-excitation of induction machine emerged, for the first time in 1935, when Basset and Potter reported that the induction machine can be operated as an induction generator in isolated mode by using external capacitor [2]. Wagner (1939) gave an approximate method of analysis of self-excited induction generator by separating the real and reactive parts of the circuit [3]. The use of series capacitor for the analysis was also reported by Wagner (1941) to improve voltage across the load and presented systematic analysis of SEIG [4].

Recent advancements in Power Electronics have made it possible to regulate the SEIG in many ways, which has resulted in an increased interest in the use of induction generators for small scale power generation with wind power and low hydro heads [5]. Various researchers have used conventional techniques, which involve cumbersome mathematical procedures for steady state performance evaluation of self-excited induction generator [6-8]. Bhim studied the effect of variable speed operation employed in case of an isolated induction generator operation to feed frequency insensitive loads [9]. Sandhu and Jain suggested new equivalent circuit model for the analysis, which resulted in only quadratic equation for slip instead of fourth or higher order polynomial solutions to predict the behaviour of SEIG [10].

At present application of Artificial Intelligence techniques are gaining importance in the field of engineering. Artificial Neural Networks are one of the computational tools, which try to mimic the method of computation adopted by human brain and are bestowed with the features of human like intelligence. Analysis using Artificial Neural Networks (ANNs) technique does not require rigorous modelling as required in conventional methods. The most commonly used neural network is the Multilayer Perceptron (MLP), a feed-forward network. The neural networks are trainable but these black-box models are able to identify a system through its input-output data, without having any knowledge of the physical insights of the system. From the literature survey carried out, it is clear that Artificial Neural Networks are being applied to study and analyze the behaviour of Electrical machines. Siva et al. used Artificial Neural Networks for estimation of System Bus Voltage in power system [11].

Goel and Bhanot developed Successive Over-Relaxation Resilient Back propagation (SORRPROP) algorithm, which is extremely fast in comparison to conventional backpropagation algorithm for training of ANNs [12]. Chaturvedi et al. used Error Backpropagation gradient descent learning algorithm for training the Neural Network Models for electric machines to map complicated functions [13]. Here, an attempt has been made to introduce ANNs for performance prediction of induction generators. Artificial Neural Networks have been used to evaluate the generated voltage and frequency of SEIG running at different speeds with different values of exciting capacitance and load.

2. STEADY STATE ANALYSIS OF SEIG

Equivalent circuit model has been used for steady state analysis of Self-Excited Induction Generator [10]. Figure 1 gives per phase equivalent circuit of SEIG, showing voltage generated by rotor as an active source.

[FIGURE 1 OMITTED]

Where;

[R.sub.1], [X.sub.1] = stator resistance and reactance.

[R.sub.2], [X.sub.2] = rotor resistance and reactance referred to stator.

R, [X.sub.c] = load resistance and capacitive reactance.

[X.sub.m] = saturated reactance of induction generator.

a = ratio of generated to rated frequency.

b = ratio of actual rotor speed to synchronous speed corresponding to rated frequency.

s = slip of machine.

[E.sub.1] = air gap voltage per phase at rated frequency.

[E.sub.a] = a[E.sub.1], air gap voltage per phase at generated frequency.

[E.sub.a](1+s) is the source voltage corresponding to mechanical power transformed to electrical power through rotor and V is the output voltage.

All quantities referred above are in per unit values. Parallel combination of load resistance R and capacitive reactance [X.sub.c] results into per phase series resistance [R.sub.L] and reactance [X.sub.L]. The values of [R.sub.L] and [X.sub.L] in terms of load resistance R and capacitive reactance [X.sub.C] are given below:

[R.sub.L] = R[X.sub.C.sup.2] / ([a.sup.2][R.sup.2] + [X.sub.C.sup.2]

[X.sub.L] = a[R.sup.2][X.sub.C] / ([a.sup.2][R.sup.2] + [X.sub.C.sup.2]

From Figure 2 net impedance [Z.sub.L] across EF becomes:

[Z.sub.L] = [R.sub.L]- j[X.sub.L]

(-ve sign indicates capacitive effect)

[FIGURE 2 OMITTED]

Combining rotor impedance, net impedance across CF can be written as:

[R.sub.1L] = [R.sub.1] + [R.sub.L]

[X.sub.1L] = a[X.sub.1] - [X.sub.L] ([X.sub.L] > a[X.sub.1])

Nodal analysis of the circuit in figure 2, seen from node C gives two equations by separating the real and imaginary components:

Real part:

[R.sub.1L]/([R.sub.1L.sup.2] + [X.sub.1L.sup.2]) - s[R.sub.2]/([R.sub.2.sup.2] + [s.sup.2][a.sup.2][X.sub.2.sup.2]) = 0 ... (1)

Imaginary part:

[s.sup.2]a[X.sub.2]/([R.sub.2.sup.2] + [s.sup.2][a.sup.2][X.sub.2.sup.2]) - [X.sub.1L]/([R.sub.1L.sup.2] + [X.sub.1L.sup.2]) - 1/a[X.sub.m] = 0 ... (2)

Simplifying equation (1), the following quadratic equation in terms of slip is developed:

A[s.sup.2] + Bs + C = 0 ... (3)

where;

A = [a.sup.2] [X.sub.2.sup.2] [R.sub.1L]

B = -[R.sub.2] ([R.sub.1L.sup.2] + [X.sub.1L.sup.2])

C = [R.sub.2.sup.2] [R.sub.1L]

Equation (1) & (2) result into evaluation of [X.sub.m].

[X.sub.m] = -[R.sub.2] ([R.sup.2.sub.1L] + [X.sup.2.sub.1L])/(s[a.sup.2] [X.sub.2][R.sub.1L] + a[R.sub.2][X.sub.1L]) ... (4)

The relation between a & b can be written as: a = b/(1 + s) ... (5)

Now, unknown values of magnetizing reactance '[X.sub.m]' and p.u frequency 'a' are obtained by solving equations 1 to 5. Further, computed value of [X.sub.m] can be used to determine the air gap voltage '[E.sub.a]' using magnetizing characteristics of the machine [Appendix-I]. Computation of [E.sub.a] for given value of operating speed 'b', exciting capacitance 'C' and load resistance 'R' lead to complete solution of equivalent circuit.

2. ARTIFICIAL NEURAL NETWORKS--THE BASICS

ANNs incorporate the two fundamental components of biological neural nets i.e. Neurons (nodes) and Synapses (weights). Neurons are arranged in different layers. The input layer, contains neurons equal to number of input variables and output layer contains the neurons equal to the number of output variables. The number of neurons in the hidden layer forms different structures and have different mapping capabilities. There is a need to choose an appropriate number of neurons in hidden layer so as to get the optimal performance from the neural network. Figure 3 (a) represents the arrangement of neurons and their inter-connections in different layers. Data is presented to input layer and then passed on to hidden layer. After processing, the data is passed on to output layer. In Feed-Forward Neural Networks (FFNNs) the information processing is unidirectional, parallel and distributed. The input to any neuron is processed through squashing function to give output between the limits 0 and 1 that is depicted from figures 3 (b) & (c). Output of any neuron is given as:

g(a) = 1/ ( 1 + [e.sup.-a] ), where 'a' is the sum of weighted output of the previous layer.

[FIGURE 3 OMITTED]

4. SIMULATION DETAILS

The ANN model of SEIG was implemented using Multilayer Perceptron (MLP) network. It is known that ANNs with only one hidden layer can approximate any function to any degree of accuracy provided it has sufficient number of neurons in the hidden layer. Therefore only one hidden layer has been used in the MLP network. The input layer has three neurons accounting for three inputs namely: speed of prime mover; b, load resistance; R and capacitance; C. The output layer has two neurons that account for the two outputs namely: terminal voltage; V and frequency; f. The hidden layer was chosen to have seven neurons, hence MLP architecture for ANN used is 3-7-2.

Test machine [Appendix-I] has been used to obtain experimental data for training purpose as well as for experimental verification of computed results obtained from trained ANN. The performance of SEIG at variable speed, exciting capacitance and with different loads was first evaluated experimentally to obtain four sets of input-output data required for training of ANN. Table 1 gives the details of each data set taken on test machine. The range of speed and value of terminal capacitance have been chosen to enable the machine to supply power to the connected load at rated voltage. The resistive load is not sensitive to change in frequency. Therefore, the two values of load resistance were chosen arbitrarily. Twelve experimental input-output observations have been taken for each set. Out of these, six samples from each set (i.e. a total of 24 samples) have been used for training the neural network. 24 samples (other than training samples), six from each set have been used to verify the results from the trained ANN model.

Successive Over-Relaxation Back Propagation (SORRPROP) training algorithm is used for training the ANN [12]. SORRPROP is modified version of RPROP [14] and makes use of successive over-relaxation principle to increase convergence speed of the network. The Sum Squared Error (SSE) goal has been set at 0.000075. The initial learning rate for training of the network is kept as 0.01 for both the hidden and the output layer.

5. RESULTS AND DISCUSSION

Four sets of experiments were conducted on the test machine to obtain experimental data for verification of proposed ANN performance with given values of excitation capacitance, operating speed and load resistance.

Tables 2 to 5 give the comparison of results obtained from the trained ANN model, analytical method described in section II with experimental data. The experimental data for testing of trained ANN is different than the training data. The Sum-Square-Error obtained for analytical and ANN solutions with reference to experimental data is also included in the tables.

For first set of results (Table 2), it is observed that although the SSE value for frequency in case of analytical and ANN solutions do not differ much. But, SSE value with reference to experimental results for voltage obtained from conventional technique is very large (12.7368) compared to that for ANN solution (4.6131). For the 2nd set of test samples (Table 3), SSE of analytical analysis in case of voltage with reference to experimental results is about 50 times and that of frequency is 20 times as compared with the SSE of ANN solutions.

For 3rd set of test samples (Table 4), the SSE values obtained from analytical solution are observed to be 25 times & 8 times higher than that of ANN results for voltage and frequency respectively. Similar trends (Table 5) have been observed in the 4th set of testing samples.

A close agreement between experimental and ANN simulation results prove the validity of ANN modelling. Moreover, ANN model results are found to be far superior in comparison with conventional computational techniques. Further, ANN model of SEIG does not require any assumptions and complex mathematical computations unlike in conventional analytical techniques. It only needs experimental data for training. Nowadays, with the use of precision measuring instruments, large amount of experimental data can be obtained and therefore, accuracy of ANN model can be improved further by increasing the number of training samples.

Effect of speed on output voltage of SEIG with different values of capacitance and load resistance is shown in figures 4 and 5. It is established that higher value of capacitance lowers the speed requirements to generate rated voltage at particular load. But at lower speeds the output frequency decreases, thus capacitance and operating speed have interdependence to generate rated voltage and frequency. Further from figure 6, it is clear that SSE of ANN model with reference to experimental results is very small as compared to the SSE of analytical results. This establishes the superiority of ANN model over conventional analytical techniques.

[FIGURES 4-6 OMITTED]

6. CONCLUSIONS

Self-excited induction generators are found to be very useful for remote and windy areas in case terminal voltage and frequency are controllable. This can be achieved with prior estimation of performance of induction machine as generator. In this paper, ANN model has been implemented to predict the effect of speed, capacitance and load resistance on generated voltage and frequency of Self-Excited Induction Generator (SEIG). It is seen that the analysis carried out using ANN model is more accurate in comparison to conventional computational techniques. From the difference in SSE values of the ANN solution and the analytical method, it is concluded that ANN technique is superior in comparison to conventional analytical method. Further, ANN model of SEIG does not require any assumptions and complex mathematical computations. By increasing the number of training samples, the accuracy of ANN model can be further improved.

Appendix--I

Machine Specifications:

3-Phase, 50 Hz, 2.2 KW/3.0 HP, 4-pole, 230 Volts, 8.6 Amp. Delta connected squirrel cage induction machine.

Machine Parameters:

[R.sub.1] = 3.35 [ohm] [R.sub.2] = 1.76 [ohm] [X.sub.1] = 4.85 [ohm]

[X.sub.2] = 4.85 [ohm]

Magnetization characteristics of machine for determination of air gap voltage:

[E.sub.1] = 344.411 - 1.610 [X.sub.m] [X.sub.m] < 82.292

[E.sub.1] = 465.120 - 3.077 [X.sub.m] 95.569 > [X.sub.m] [greater than or equal to] 82.292

[E.sub.1] = 579.897 - 4.278 [X.sub.m] 108.00 > [X.sub.m] [greater than or equal to] 95.569

[E.sub.1] = 0 [X.sub.m] > 108.00

Received: Jan. 2006. Accepted: Jun. 2006.

REFERENCES

[1] R. C. Bansal, T. S. Bhatti, and D. P Kothari," Energy Conversion and Management", Vol. 43, 2002, pp 2175-2187.

[2] E. D. Basset, F. M. Potter, "Capacitive excitation for induction generator", AIEE Transactions. (Elect. Eng.), Vol. 54, 1935, pp 540-545.

[3] C. F. Wagner, "Self-excitation of induction motors", AIEE Transactions. (Elect. Eng.) Vol.58, 1939, pp 47-51.

[4] C. F. Wagner, "Self-Excitation of Induction Generator with Series Capacitors", Transactions. AIEE, Vol. 60, 1941, pp 1241-47

[5] S. Rajakauna and R. Bonert, "A Technique for the Steady State Analysis of Self-Excited Induction Generator with Variable Speed", Transactions on Energy Conversion, Vol. 8, No.4, 1993.

[6] S. S. Murthy, O. P. Malik and A. K. Tandon, "Analysis of Self Excited Induction Generators", Proceedings IEE, Vol. 6, part 129, 1982, pp 260-265.

[7] N. H. Malik, S. E. Haque, "Steady State Analysis and Performance of an Isolated Self-Excited Induction Generator", IEEE Transactions on Energy Conversion, Vol.3, 1986, pp 134-139.

[8] T. F. Chan, "Steady State Analysis of Self Excited Induction Generator", IEEE Transactions on Energy Conversion, Vol. 9, (2), 1994, pp 288-296.

[9] Bhim Singh, "Induction Generator--A Prospective", Electric Machines and Power Systems, Vol. 23, 1995, pp 163.

[10] K. S. Sandhu and S. K. Jain, "Operational Aspects of SEIG Using a New Model", Electric Machines and Power Systems, Vol. 27, 1999, pp 169-180.

[11] Siva PrakashVelpula and Biswarup Das, "Distribution System Bus Voltage Estimation Using ANN", Proc. of International Conf. on Computer Application in Electrical Engineering, Recent Advances, IIT-Roorkee,2002.

[12] A. K. Goel and S. Bhanot, "Modeling of Continually Stirred Tank Heater With ANNs Using Successive Over-Relaxation Backpropagation Algorithm", in Asian Control Conference ASCC2002 held at Singapore in 2002, pp 614-617

[13] P. K. Chaturvedi, P. S. Satsangi, and P. K. Kalra, "Flexible Neural Network Models for Electric Machines", Inst. of Engineers, Vol. 80, 1999.

[14] M. Riedmiller and H. Braun, "A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm", ICNN' 93, Proceedings of the Annual ICNN Conference (San Francisco: CA), pp. 586-591.

Raja Singh Khela, Raj Kumar Bansal, K. S. Sandhu * and Ashok Kuram Goel

Dept. of Electrical Engg., GZS College of Engg. & Tech. Bathinda, Punjab PIN--151 001, Tel: +91-164-2281745, Fax: +91-164-2280164, Email: rskhela@rediffmail.com

* Dept. of Electrical Engg., National Institute of Technology, Kurukshetra, Haryana PIN--136 119, Tel: +91-1744-238470-ext-309. Fax: +91-1744-238050.
Table 1. Range of Input Variables for Experimental Data.

 Speed RPM Load
Sr. Experiment Capacitance Resistance No. of
No. Set No. From To C ([micro]F) R ([ohm]) samples

01 Set #1 1430 1600 36 160 12

02 Set #2 1270 1450 51 160 12

03 Set #3 1400 1570 36 220 12

04 Set #4 1280 1420 51 220 12

Table 2 Set # 1 Comparison of Results

Capacitance C = 36 [micro]F

 Voltage (V)
Speed
RPM Analytical Expt. ANN

1433 134.1368 134 134.46
1467 158.3876 158 157.48
1498 178.4280 176 177.81
1516 188.0909 189 188.86
1543 202.4747 203 203.87
1596 230.3602 228 228.20
SSE * 12.7368 -- 4.6131

Load Resistance R = 160 [ohm]

 Frequency (f)
Speed
RPM Analytical Expt. ANN

1433 47.1745 47.19 47.19
1467 48.2894 48.30 48.30
1498 49.3056 49.35 49.31
1516 49.8955 49.92 49.89
1543 50.7802 50.74 50.78
1596 52.5161 52.54 52.54
SSE * 0.0051 -- 0.0041

Table 3. Set # 2 Comparison of Results

 Capacitance C = 51 [micro]F

 Voltage (V)
Speed
RPM Analytical Expt. ANN

1280 163.8196 166 166.24
1321 185.4419 187 186.66
1353 199.2042 201 200.80
1390 212.0390 215 215.16
1440 229.2695 232 232.50
1445 230.9866 234 233.88
SSE * 49.0072 -- 0.5058

 Load Resistance R = 160 [ohm]

 Frequency (f)
Speed
RPM Analytical Expt. ANN

1280 42.1136 42.17 42.15
1321 43.4553 43.50 43.54
1353 44.5020 44.67 44.64
1390 45.7116 45.91 45.87
1440 47.3451 47.40 47.43
1445 47.5084 47.55 47.55
SSE * 0.1177 -- 0.0054

* SSE : Sum-Square Error with reference to experimental results

Table 4 Set # 3 Comparison of Results

Capacitance C = 36 [micro]F Load

 Voltage (V)
Speed
RPM Analytical Expt. ANN

1403 129.7862 123 122.97
1442 157.9313 154 153.71
1467 174.5763 171 171.13
1496 190.3046 188 186.79
1540 213.8753 210 211.45
1563 227.1258 224 223.79
SSE * 104.3967 -- 3.7234

Load Resistance R = 220 [ohm]

 Frequency (f)
Speed
RPM Analytical Expt. ANN

1403 46.3343 47.04 47.04
1442 47.6181 47.64 47.90
1467 48.4409 48.28 48.37
1496 49.3951 49.24 49.40
1540 50.8424 50.78 50.80
1563 51.6644 51.13 51.12
SSE * 0.8379 -- 0.1018

Table 5. Set # 4 Comparison of Results

Capacitance C = 51 [micro]F Load

 Voltage (V)
Speed
RPM Analytical Expt. ANN

1285 175.9696 174 173.90
1315 191.8326 187 187.36
1350 204.1371 202 202.37
1386 216.7150 216 216.93
1406 223.6741 223 224.77
1430 232.0025 237 236.92
SSE * 57.7408 4.3024

Load Resistance R = 220 [ohm]

 Frequency (f)
Speed
RPM Analytical Expt. ANN

1285 42.4105 42.43 42.43
1315 43.3960 43.41 43.44
1350 44.5452 44.50 44.59
1386 45.7268 45.70 45.80
1406 46.3829 46.41 46.49
1430 47.1701 47.62 47.62
SSE * 0.2065 -- 0.0254

* SSE : Sum -Square Error with reference to experimental results
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Author:Khela, Raja Singh; Bansal, Raj Kumar; Sandhu, K.S.; Goel, Ashok Kumar
Publication:Journal of Computer Science & Technology
Date:Oct 1, 2006
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