Optimal design of lightning pulse generators for the experimental study of indirect effects in avionic systems

Abstract

In this paper we propose a procedure to design pulse generators for the simulation of lightning indirect effects in avionic systems. A genetic algorithm is used to identify the generator parameters for different strength levels to obtain high accuracy of the voltage and current waveforms in comparison to the international standards requirements. A dedicated experimental set-up is used to evaluate the accuracy and the effectiveness of the optimization procedure. Measured and computed data are compared and discussed.

Keywords

Optimal design genetic algorithm electromagnetic compatibility lightning

1. Introduction

The use of electronic and electromechanical equipments to improve performances and comfort of aircrafts is rapidly increasing in these last years. Possible faults of these devices can be critical for the flight safety, therefore accurate design and qualification procedures have to be carried out to satisfy the functional requirements under different environmental conditions. A complete electromagnetic compatibility qualification is important, where several test are performed to evaluate the electromagnetic emissions and the susceptibility of the electronic and electromechanical equipments. A dedicate international standard was developed for this aim [1, 2]: in that document environmental conditions, instruments and procedures are discussed and specified, in order to perform the suitable electromagnetic compatibility tests. Among them one of the most critical is the so called indirect lightning test, where the effects on the electric power plant of an aircraft, after a lightning shot, are simulated. The standard procedure indicates different waveforms and amplitudes for the induced lightning pulses in order to simulate indirect lightning under different conditions. In addition the waveform requirements are changing in time with the successive standard revisions. For these reasons different lightning generators have to be used. In this paper we propose a design procedure for the lightning generators to optimize their performances. The papers presented in literature propose in general empirical formulas to obtain the generator network parameters [3, 4, 5, 6]. The validity of these formulas are limited to specific circuits. In our work we propose a more general approach, that can be used for different circuits of lightning generation tests. The procedure is based on a genetic algorithm to obtain the optimal values of the electrical parameters of the generator for a given waveform. The method was validated by a comparison between the experimental results and the standard waveform requirements.

Table 1
Levels of waveforms 4 and 1

Level	Waveform 4 – Voc			Waveform 1 – Isc
	Peak [V]	t ${}_{1}$ [ $\eta$ s]	t ${}_{2}$ [ $\eta$ s]	Peak [A]	t ${}_{1}$ [ $\eta$ s]	t ${}_{2}$ [ $\eta$ s]
1	50	6.4 $\pm$ 20%	69 $\pm$ 20%	10	6.4 $\pm$ 20%	69 $\pm$ 20%
2	125			25
3	300			60
4	750			150
5	1600			320

Figure 1.

Voltage and current waveform 1 and 4 of the section 22 of [1].

2. Lightning induced waveforms and standard requirements

In this work we have considered the pin injection method and the waveforms 1 and 4 specified in the Section 22 of the standard [1]. Before the tests a calibration procedure have to be done, by reproducing these waveforms. We have defined an optimization procedure for the identification of the parameters of the lightning generator to be used in this case. The identification procedure can be easily extended to other injection methods and waveforms. The waveform 1 is the current waveform generated when the lightning generator is in short circuit condition (Isc), while the waveform 4 is the voltage waveform generated when the lightning generator is in open circuit condition (Voc). The typical waveform parameters are indicated in the Fig. 1. The value of the waveform level, the rise time and the fall time, in agreement with the standard [1], are reported in the Table 1. Different values of the waveform levels are specified for different positions of the equipment under test (EUT) inside the aircraft. The equipments placed close to the external structure of the aircraft have to be tested using the higher waveform levels, while the tests related to the equipments placed in the protected area are referred to the lower waveform levels.

During the pin injection test the injection of the lightning induced current is made directly into the pins of the EUT connector, in general between each pin and the case ground. This test is used for assessing the dielectric withstand and the damage tolerance of the equipment circuit interface.

3. Identification of the lightning generator parameters

The lightning generator is roughly made by three parts, an high voltage supply, a capacitor and an electrical coupling net to inject the induced transient into the EUT pins. The high voltage supply is used to charge the capacitor up to a given voltage level, after that the capacitor is discharged into the EUT pins trough the coupling net. The characteristics of the Voc and Isc waveforms are function of the parameters of the capacitor and the coupling net. Different kind of coupling net can be used; one of these is represented in Fig. 2. A DC high voltage supply is used to charge the capacitor C1 trough the switch S1 closed. When a given voltage level V0 is reached the switch S1 is open and the switch S2 is closed. In this way the energy stored in the capacitor C1 is discharged trough the right part of the circuit. The parameters V0, C1, L1, R1 and R2 have to be identified in order to obtain the waveforms 4 and 1 described in the previous section, using respectively the circuit configurations shown in Fig. 2a and b. A this point the indirect lightning test can be done using the parameters identified and the test set-up presented in Fig. 2c. Different test levels can be performed using different values of the parameter V0, keeping constant C1, L1, R1 and R2.

Figure 2.

Lightning generator layout: (a) calibration set-up for the waveform 4; (b) calibration set-up for the waveform 1; (c) test set-up.

The parameters identification of this lightning generator is an inverse problem with multiple solutions and different accuracy levels respect to the standard requirements. Find the optimal solution is a very difficult task, in this section we propose a possible approach based on a genetic algorithm [7, 8, 9, 10, 11, 12]. The analytical expressions of Voc and Isc are indicated below

$\displaystyle\text{Voc}\left(\text{t}\right)=\text{R}1\frac{\text{V}0}{\left({% \alpha_{1}-\alpha_{2}}\right)\text{L}1}\left({\text{e}^{\alpha_{2}\text{t}}-% \text{e}^{\alpha_{1}\text{t}}}\right)$ (1) $\displaystyle\text{Isc}\left(\text{t}\right)=\frac{\text{Rp}}{\text{R}2}\frac{% \text{V}0}{\left({\alpha_{3}-\alpha_{4}}\right)\text{L}1}\left({\text{e}^{% \alpha_{4}\text{t}}-\text{e}^{\alpha_{3}\text{t}}}\right)$ (2)

where

$\displaystyle\alpha_{1,2}=\frac{-\text{R}1\pm\sqrt{\text{R}1^{2}-4\frac{\text{% L}1}{\text{C}1}}}{2\text{L}1};\quad\alpha_{3,4}=\frac{-\text{Rp}\pm\sqrt{\text% {Rp}^{2}-4\frac{\text{L}1}{\text{C}1}}}{2\text{L}1};\quad\text{Rp}=\frac{\text% {R}1\cdot\text{R}2}{\text{R}1+\text{R}2}$ (3)

In order to reduce the computational time of the identification procedure we have chosen C1 $=$ 100 $\mu$ F and we have identified the others four parameters. The parameters C1, L1, R1 and R2 are keeping constant, while V0 is changing for the different levels. In the genetic algorithm proposed each parameter is a gene, and the array {V0, L1, R1, R2} is an individual. We have tested different genetic algorithms in order to find the more efficient and reliable, in particular we have changed the number of individuals for each generation and the strategies to create new generations. The best approach found is presented below. First of all are fixed the ranges of existence of the four parameters, after that are chosen 100 individuals for each generation and the initial population is randomly created. The new generation at each step is improved keeping the two best values of the previous generation and defining the others by means a combination of crossover and mutation procedures. The crossover and mutation ratio was 0.5, this means that the 50% of the children is generated by a combination of the genes of a set of the best individuals of the previous generation (parents), while a 50% of the children is generated introducing new genetic material by a random changing of the parents genes. After a new generation the waveforms Eqs (1) and (2) are computed and the values of t ${}_{1}$ and t ${}_{2}$ are compared with the standard requirements specified in the Table 1. The convergence to a minimum of the displacement between the computed waveforms and the features described in the Table 1 is guaranteed after about 10 generations. The expression of the displacement is

$\displaystyle\text{D}=\frac{\left|{\text{t}_{1\text{Vc}}-\text{t}_{1\text{Vs}}% }\right|}{\text{t}_{1\text{Vs}}}+\frac{\left|{\text{t}_{2\text{Vc}}-\text{t}_{% 2\text{Vs}}}\right|}{\text{t}_{2\text{Vs}}}+\frac{\left|{\text{t}_{1\text{Ic}}% -\text{t}_{1\text{Is}}}\right|}{\text{t}_{1\text{Is}}}+\frac{\left|{\text{t}_{% 2\text{Ic}}-\text{t}_{2\text{Is}}}\right|}{\text{t}_{2\text{Is}}}$ (4)

where t ${}_{1\text{Vc}}$ and t ${}_{2\text{Vc}}$ are t ${}_{1}$ and t ${}_{2}$ for the voltage pulse computed, t ${}_{1\text{Vs}}$ and t ${}_{2\text{Vs}}$ are t ${}_{1}$ and t ${}_{2}$ for the voltage pulse standard specified in Table 1, t ${}_{1\text{Ic}}$ and t ${}_{2\text{Ic}}$ are t ${}_{1}$ and t ${}_{2}$ for the current pulse computed, t ${}_{1\text{Is}}$ and t ${}_{2\text{Is}}$ are t ${}_{1}$ and t ${}_{2}$ for the current pulse standard specified in Table 1. The CPU time to do that is about 280 seconds using CPU INTEL© Core i7-3610QM. The results obtained are presented in the Table 2. In the next sections an experimental validation and a discussion of the proposed approach is presented.

Table 2

Results of the identification procedure

Level	V0 [V]	C1 [ $\mu$ F]	L1 [ $\mu$ H]	R1 [ $\Omega$ ]	R2 [ $\Omega$ ]
1	52.5	100.0	1.6	1.08	4.9
2	132.0
3	316.5
4	791.0
5	1685.0

Table 3

Main characteristics of the experimental set-up shown in Fig. 3

(a)	Autotransformer, Belotti, model V-20NP, 230 V/0-230 V, 10 A.
(b)	Transformer elevator, Advance Transformer Co., model 8103N44-11, 230 V/2500 V.
(c)	High voltage AC/DC converter, diode bridge and leveling capacitor.
(d)	4 Capacitors, ICAR, model LNK-P2X-100-90, 100 $\mu$ F $\pm$ 10%.
(e)	Electronic Switch S2, POSEICO, Phase Control Thyristor, mod AT636, 1800 V, 1965 A
(f)	Inductance L1, air coil with 7 turns, diameter 2 cm.
(g)	Resistance R1, wire resistor, 1 $\Omega$ $\pm$ 5%.
(h)	Resistance R2, wire resistor, 4.9 $\Omega$ $\pm$ 5%.

Figure 3.

Experimental set-up of the lightning generator.

4. Experimental validation of the proposed approach

To prove the reliability of the genetic algorithm presented above for the parameters identification of a lightning generator, a dedicated experimental set-up is performed to generate the waveforms 4 and 1 from level 1 to 5. In Fig. 3 a picture of the experimental set-up is shown. The DC high voltage supply has three connected parts, (a) is an autotransformer to drive the voltage input of the transformer elevator (b), while the rectifier (c) converts the alternate current from the output of (b) in a direct current to charge the capacitor bank. The capacitor bank (d) is discharged trough the electronic switch (e) on the coupling net, made by an inductor (f), and the resistor (g) and (h). The main characteristics of these components are shown in Table 3. The voltage and current pulses are measured using the oscilloscope Tektronix TDS2024B, the high voltage probe Tektronix P6013 and the current probe Pearson Electronics 3525. The sample rate used has been up to 100 Ms/sec.

Figure 4.

Comparison between computed data, experimental data and standard constraints in the open circuit calibration.

Figure 5.

Comparison between computed data, experimental data and standard constraints in the open circuit calibration (rise time).

Figure 6.

Comparison between computed data, experimental data and standard constraints in the short circuit calibration.

Figure 7.

Comparison between computed data, experimental data and standard constraints in the short circuit calibration (rise time).

Figure 8.

Open circuit waveforms for the levels 1 to 5.

Figure 9.

Short circuit waveforms for the levels 1 to 5.

5. Results and discussion

In the Figs 4–7 a comparison between the calibration curves computed and measured with the standard constraints for the level 5 is reported. In particular in the Figs 4 and 6 are presented the overall waveforms respectively in the open circuit calibration (see Fig. 2a) and in the short circuit calibration (see Fig. 2b), while in the Figs 5 and 7 are highlighted the two corresponding rise times. The differences between the computed data, using the Eqs (1)–(3) with the identified values of the parameters, and the measured data using the experimental set-up presented in the previous section, are mainly due to the parasitic parameters of the circuit and the uncertainty of the component values, indicated in Table 3. In particular the parasitic inductance of the circuit is very critical: for this reason it is very important the use of tick and short interconnecting wires between the circuital components. Following this indication the accuracy of the lighting generator waveforms results more than satisfactory as indicated in the Figs 8 and 9 for the level 1 to 5. The highest test levels can generate damages for the components of the lightning generators because of the high values of voltages and currents. In the our experiments we have verified that the components used for the lightning generator listed in the Table 3, ensure robustness and repeatability of the waveforms up to level 5 without degradation of performances after many tests.

6. Conclusions

In this paper a possible approach to identify the generator parameters for the simulation of the indirect effects of lightning shots in avionic environment has been proposed. The accuracy and the reliability we get with this approach seems to be satisfactory compared to the standard requirements. In the paper only an example about the waveforms 1 and 4 of the standard [1] is presented, but the proposed approach can be extended to the other waveforms 2, 3, 5A and 5B, or to other similar test procedure where a pulse generator is involved, according to the different standards or custom requirements.

Footnotes

Acknowledgments

This work was partially supported by Fondazione CARIT Cassa di Risparmio di Terni e Narni (Italy).

References

RTCA Incorporated, RTCA/DO-160G – Environmental Conditions and Test Procedures for Airborne Equipment, Washington, DC 20036 (USA), December 8, 2010.

RTCA Incorporated, RTCA/DO-357, User Guide: Supplement to DO-160G, Washington, DC 20036 (USA), December 16, 2014.

Wang

Z.C.

and Yan

N.N.

, Design of multi-component impulse current generator for practical lightning current simulation, in: 2014 International Conference on Lightning Protection (ICLP), Shanghai, 2014, pp. 278–282.

Wang

Huang

Chen

and Sun

, Design and implementation of continuous multiple impulse current generator for aircraft lightning protection tests, in: 2012 International Conference on High Voltage Engineering and Application, Shanghai, 2012, pp. 89–91.

Sato

Harada

and Hanai

, IEC 60060-1 Requirements in Impulse Current Waveform Parameters, in: 2005 International Power Engineering Conference, Singapore, 2005, pp. 1–5.

Mazzetti

Capasso

and Ratti

, HV Impulse Generators Equivalent Circuits, in IEEE Transactions on Power Apparatus and Systems PAS-91(5) (Sept. 1972), 2161–2170.

Salvini

and Fulginei

F.R.

, Genetic algorithms and neural networks generalizing the Jiles-Atherton model of static hysteresis for dynamic loops, in IEEE Transactions on Magnetics 38(2) (Mar 2002), 873–876.

Salvini

Fulginei

F.R.

and Coltelli

, A neuro-genetic and time-frequency approach to macromodeling dynamic hysteresis in the harmonic regime, in IEEE Transactions on Magnetics 39(3) (May 2003), 1401–1404.

Salvini

Fulginei

F.R.

and Pucacco

, Generalization of the static Preisach model for dynamic hysteresis by a genetic approach, in IEEE Transactions on Magnetics 39(3) (May 2003), 1353–1356.

10.

Kumar

Dalal

and Singh

A.K.

, Identification of three phase induction machines equivalent circuits parameters using multi-objective genetic algorithms, in: Electrical Machines (ICEM), 2014 International Conference on, Berlin, 2014, pp. 1211–1217.

11.

Sundareswaran

Shyam

H.N.

Palani

and James

, Induction motor Parameter Estimation using Hybrid Genetic Algorithm, in: 2008 IEEE Region 10 and the Third international Conference on Industrial and Information Systems, Kharagpur, 2008, pp. 1–6.

12.

Escarela-Perez

Niewierowicz

and Campero-Littlewood

, Synchronous Machine Parameters from Frequency-Response Finite-Element Simulations and Genetic Algorithms, in IEEE Power Engineering Review 21(5) (May 2001), 61–61.

Optimal design of lightning pulse generators for the experimental study of indirect effects in avionic systems

Abstract

Keywords

1. Introduction

Table 1 Levels of waveforms 4 and 1

3. Identification of the lightning generator parameters

6. Conclusions

Footnotes

Acknowledgments

References

Table 1
Levels of waveforms 4 and 1