Васильева Ю. З.

Национальный исследовательский Томский политехнический университет

Designing of digital band-pass filter for synchronous generator diagnostic system

The necessity of developing digital band-pass filter at creation of synchronous generator diagnostic system of turn-to-turn short circuit rotor winding, based on the harmonic component separation from the signal obtained in the output of the magnetic field sensor [1]. A problem complexity is the low value of the intelligence signal - 1.5 ... 3% of the fundamental harmonic, and it is also a large number of noise (pulse noises, higher harmonic components, etc.) [2].

Statement of objectives: to develop the minimal order digital band-pass filter capable of suppressing constant and higher harmonic components, pass and amplify the signal with frequency equal to the rotor frequency.

There was a problem to dedicate the signal being proportional to the value of sinusoidal half-waves asymmetry during the diagnostic system development.

For example, Figure 1 shows a perfect EMF signal from the sensor output. The signal asymmetry is manifested in the decreasing of the one of the 2p half-waves amplitude (∆е) (Figure 1, p = 1), where p is machine pole pairs number.

Figure 1. The sensor signal data in case of a SG damage

The problem was solved by EMF converting into a unipolar signal, followed by the band-pass dedicating of the subharmonic frequency f₁=f_s/p, where f_s is the network frequency. The digital band-pass filter (BPF) consisting of the high pass filter (HPF) and low pass filter (LPF) is necessary to dedicate the subharmonic frequency f_1.

The level of the BPF useful signal increases with increasing LPF order, the filter response time also increases. It has a negative impact on the device operating speed.

Special requirements to the HPF order was not made in the PS development. The smallest filter order N was the choice criterion for required level of noise suppression.

The required level is determined by the ratio of useful signal level to general signal level:

The calculation showed that the required attenuation level was equal 60 dB at the minimum level of the selected signal was 1.5% of the total.

The Chebyshev filter, Butterworth and elliptic filters were selected as the LPF basis. The each selected filter order was calculated according to the formulas (1), (2), (3) at the suppression level R_S = 60 dB [3,4].

The Butterworth filter order

(1)

The Chebyshev filter order

(2)

The Cauer filter order

(3)

where, N_b, N_ch, N_k – are Chebyshev, Butterworth and elliptic filters orders, R_P – is the signal distortion level in the pass-band, R_S –is the noise suppression level, ω₀– is a passband, ω₁ – is a rejection frequency, К – is a complete elliptic integral, – is a complementary elliptic integral.

The dependence of the filters order from the useful signal level Δe at the given suppression level is shown in Figure 2.

Figure 2. The dependence of the filters order from the useful signal
level Δe at R_S = 60 dB

(1 - by Butterworth 2 - by Chebyshev, 3 - by Cauer)

As evident from the figure 2, the minimum order value N_k of elliptic filter is equal to 5 in case of R_S=60 dB and Δe =1,5 % . The BPF was implemented based on the elliptic filter. A distortion of the useful signal in the passband amounted to
0.5 dB.

The BPF consists of the high-pass and low-pass filter component, which can be represented as the following transfer function:

where H(s) is the transfer function, s is the complex variable, a_i,b_i are the transfer function coefficients. The BPF transfer function coefficients values for the above example are shown in Table 1.

Table 1. The BPF coefficients

LPF	a0	a1	a2	a3	a4	a5
	7,994·10^11	0	3,168·10^6	0	2,62	0
	b0	b1	b2	b3	b4	b5
	7,988·10^11	9,204·10^9	4,652·10^7	2,08·10^5	376,5	1
HPF	a0	a1	a2	a3	a4	a5
	0	3,101·10^8	0	3,852·10^4	0	1
	b0	b1	b2	b3	b4	b5
	1,168·10^13	4,457·10^10	2,497·10^8	5,66·10^4	1,136·10^3	1

The BPF experimental test was carried out on synchronous generator GAB-4-T/230 at the laboratory. Filter characteristics coincided with the calculated values. It has allowed to reveal reliably not less than 2% of short circuits in generator various operating modes.

Сonclusions

1. The designed filter fully meets the requirements of the synchronous generator diagnostic system;

2. The band-pass filter designing method is justified for synchronous generator diagnostic system;

3. The efficiency of operation designed filter is experimentally confirmed.

The list of references:

1. Gutnikov V.S. Filtraciya izmeritelnyh signalov [Filtration of measuring signals]. – L.: Energoatomizdat, – 1992. – 192p.

2. Polishсhuk V.I., Novozhilov A.N. Ustrojstvo zashchity sinhronnoj elektricheskoj mashiny ot vitkovyh i dvojnyh na zemlyu zamykanij v obmotke rotora [Protection device of synchronous electric machine against turn-to-turn and double earth fault in the rotor winding]//Patent № 22450 (KZ). Official bulletin. Prom . Property. 2010, no. 4.

3. Polishchuk V.I. Postroenie zashchity ot vitkovogo zamykaniya v obmotke rotora sinkhronnogo generatora na osnove induktsion-nogo datchika magnitnogo polya rasseyaniya [Construction of protection interturn fault in the winding of synchronous generator rotor based on inductive sensor magnetic stray field]. Bulletin of the Tomsk Polytechnic University, 2012, vol. 321, no. 4, pp. 57-61.

4. J. D. Rhodes Teoriya elektricheskih filtrov [Theory of Electrical Filters]. – M.: Sov. radio, – 1980. – 240p.