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14 ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, Nr. 1, ianuarie-martie 2013 Inductive Sensor Parameters Important for Partial Discharge Measurement Jozef BALOGH, Jaroslav PETRÁŠ∗ Abstract Monitoring of partial discharge activity in insulation systems of high voltage and very high voltage electric power devices can be made by galvanic method, but additionally there are alternative methods, such as measurement by inductive sensors or acoustic method. For inductive indirect method we needed to design linear sensors that are ideal for partial discharge source localization and toroidal sensors that are used for partial discharge activity measurement due to their electro-magnetic and geometric parameters. In order to test parameters of these sensors we had to find a method to measure them. (Parameters of inductive sensors for partial discharge activity measurement). Keywords: toroidal sensor, induction sensor, partial discharges 1. Introduction Partial discharge measurement is one of the often used methods of insulation system diagnostics. This method has a fixed place in the set of diagnostic measurement methods used for insulation system condition determination in high voltage electric power devices [8,10]. We developed inductive sensors for partial discharge detection and monitoring in insulation systems which have two different construction types: linear [1] and toroidal type [2], [3]. Inductive toroidal sensors are used for leakage current measuring at frequency of 50 Hz and they are connected into working grounding of the object under test. They exploit a current changer function. A signal from sensor winding on toroidal ferromagnetic core is furthermore evaluated by computer technology. 2. Toroidal sensor principle A toroidal inductive sensor is designed with respect to its location and placement, shape and way of connection into working grounding circuit of the measured object. Supposing two current circuits that are ∗ Jozef BALOGH, PhD., TU Košice, FEI, Department of Electric Power Engineering, Mäsiarska 74, 040 01 Košice, Slovak Republic, [email protected] Jaroslav PETRÁŠ, Ing. PhD., TU Košice, FEI, Department of Electric Power Engineering, Mäsiarska 74, 040 01 Košice, Slovak Republic, [email protected] electro-magnetically connected (Figure 1), Figure 1. Inductive toroidal sensor we can get an equation in ideal case for output voltage: u 2 = −i2 .R2 − L2 . di2 di + M 12 . 1 dt dt (1) where R2 and L2 parameters represent measurable values of effective resistance and self-inductivity of the coil, and M12 represents common inductivity between circuits 1 and 2. Outgoing from real conditions, it is obvious that the measurement of the current i1 flowing through the conductor can be made by measuring u2 voltage on the clamps of coil with winding number N2 ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, nr. 1, ianuarie-martie 2013 (secondary winding), and on input resistor Rm of the amplifier (u2=Rm.i2). Because of exactness of the measurement it is necessary that the windings were uniformly placed on the ringlet with the shape of rectangular cross-sectioned toroid. A conductor with primary current flowing through it with unknown value i1 runs through ringlet hole in arbitrary surface. The current i1 induces in secondary winding a voltage u2: u2 = − M 21. didt1 (2) This voltage u2 induces in closed secondary winding a current i2. It must be noticed that M12 = M21. Voltage u2 is equal to the sum of i2R2 voltage descent on R2 resistance and on the L2 inductance: − M 21. didt1 = i2 R2 + L2 . didt2 (3) 15 By calculation, we suppose that the current is only in secondary circuit and we search for induction flow Ψ1M supplied by this current which flows trough the surface delimited by primary circuit. If the secondary circuit is winded uniformly and relatively narrowly on the ringlet, each induction line of the flow Φ induced by current i2 runs through all the secondary windings. Each induction line of this flow enlaces once the conductor of the primary current despite of complicated shape of the conductor. In this case, the equation Ψ1Μ=Φ is valid. As can be found in Kalantarov-Nejman [5], for toroid with dimensions on Figure 1, the next equation is valid: Ψ1 M = Φ = μ 0μ r 2π . N 2 i 2 h ln r2 r1 (8) where: By integrating this equation and supposing that for i1=0 is i2=0 we can get: - permeability of vacuum (1,256.10-6 H.m-1), μr – relative permeability of magnetic core, N2 - number of secondary windings, h - toroid height, r1, r2 - inner and outer radius of the toroid. For reciprocal induction coefficient, we can write [4]: i2 = − ML221 .i1 = − k .i1 M 12 = M 21 = Voltage drop on resistor (i2R2), especially at higher frequencies, is neglectable in comparison to self induced voltage in secondary circuit. Therefore: − M 21. didt1 = L2 . didt2 (4) (5) where k is transform coefficient. If we want to calculate, it we have to know the coefficient of reciprocal induction M12, which represents the inductive acting of the first current circuit on the second circuit. The coefficient M21 is defined by equation [6]: M 21 = Ψ2M i1 (6) In order to calculate directly the reciprocal coefficient of induction M21 according to the equation above we have to define first the allover flow Ψ2M, which run through the second circuit with condition that in the first circuit flows the current i1. However the complicated shape of the primary circuit disables the straightforward calculation of the flow Ψ2M. In this case, the equation M21=M12 does a good job for us. The definition of M12 is according to: M 12 = Ψ1 M i2 (7) μ0 Ψ1Μ 2π = μ 0μ r 2π . N 2 h ln r2 r1 (9) The coefficient of self-induction L2 for winding of toroid reads: L2 = μ 0μ r 2π .N 22 h ln rr12 (10) The transform coefficient k can be expressed in this way: k= M 21 L2 = 1 N2 (11) In general, if the the primary current conductor runs trough the hole of the ringlet N1-times, the transform coefficient will be: k= N1 N2 (12) An important attribute of this alignment is that its transform coefficient does not depend on the shape of the primary current conductor. By application of the knowledge as mentioned above, we can say that all conditions for small AC current and pulse ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, Nr. 1, ianuarie-martie 2013 16 current measurement are fulfilled. Inductive sensor should be connected to the secondary winding circuit and to the circuit with high input impedance (Figure 2). Usually, the signal of partial discharge activity in insulation cavities has a pulse character and the amplitude a duration of this pulse depend on various factors. A signal emitted from insulation system can be captured by resonance circuit. On Figure 4, there is depicted a current pulse created in insulation material cavity [6]. Figure 2. Detection circuit with inductive sensor A low number of windings ensures high resistance against external noises. From the mentioned above conditions, it results that: i2 = N1 N2 .i1 (13) If N1=1, then i2 represents N2-times smaller part of the measured current i1. For operation in AC electric fields or in dynamic modes, some magnetic materials are appropriate with coercive strength Hc~800 Am-1. They are used for the weakest magnetic fields and are very easy to magnetize or demagnetize. They also have narrow hysteresis loop, high value of initial and maximal permeability (80 to 100 thousands) and small measured losses. 3. Linear sensor principle Linear sensor has to be placed into electromagnetic field of the radiated signal so that the vector of magnetic induction B and magnetic intensity H are oriented into the axis of the sensor (Figure 3). I H B Figure 4. Current pulse of streamer discharge [7] This pulse can be captured by above mentioned circuit (as seen on Figure 5). Figure 5. Transmitter and receiver of discharge current pulse signals We can solve this situation mathematically by the help of modeled circuit and Dirac function. If we replace the signal transmitter by DC source that is connected for a short time to a capacitor C, we can assume that in time t=0 a source with voltage U0 is connected (with initial conditions i(0)=0 and charge on capacitor Q(0)=0. We can solve the current in circuit in time t>0. Voltage has the shape U0δ(t). Then, the equation for the circuit is: t U L + Ri + di dt 1 C ∫ idt = U δ(t ) 0 0 Lpi + Ri + Cp1 i = U 0 .1 Figure 3. Linear shaped inductive sensor (14) ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, nr. 1, ianuarie-martie 2013 (Lp 2 + Rp + C1 )i = U 0 p 4. Conclusions p i = L ( p 2 U+ R0 pp + 1 ) = UL0 2 ( p + 2RL ) + LC1 − 4RL22 L LC We assume that: 1 R2 − 2 = ω2 LC 4 L i = UωL0 ( p+p+aa)2−+aω2 = ωUL i= U0 ωL (e − at R 2L [ p+a ( p+a)2 +ω2 17 =a − ω1 ( p+aa)ω2 +ω2 ] cos( ω t ) − ωa e − at sin( ω t ) ) These equations result in a current signal that is dumped with signal envelope e-at, as can be seen on Figure 6. a). Economical aspects have forced the usage of linear sensor type as more advantageous. Their advantage in comparison to toroidal type lies in the fact that we do not have to disconnect the circuit before measurement by linear sensor type. Using this type of sensors for partial discharge measurement can complete the widely used direct galvanic method. It is possible to measure the device without disconnecting it from operation [9]. 5. Acknowledgment We support research activities in Slovakia / Project is co-financed from EU funds. This paper was developed within the Project "Centrum excelentnosti integrovaného výskumu a využitia progresívnych materiálov a technológií v oblasti automobilovej elektroniky", ITMS 26220120055 6. References Figure 6. Current signal: a) in resonance circuit; b) signal spectrum The current i invokes on amplifier input voltage drop ΔU with the same signal shape (Figure 6). As the condition R2/4L2, 1/LC is usually fulfilled we can state that the angle velocity equals to ω ≈ 1 / LC . [1] MARTON K. a kol.: Autorské osvedčenie č. 202 129, Úrad pro vynálezy a objevy, Praha, 1976. [2] MARTON K. et al.: “Výskumná správa” GAV č.1/990345/92, EF TU Košice, 1992. [3] MARTON K., BALOGH J.: “Elektrofyzikálna analýza odozvy čiastkových výbojov modelovaných Diracovým impulzom”. Zborník, Diagnostika 93, ZČU Plzeň, 1993. [4] MARTON K. et al.: Záverečná práca rezortného výskumu R 02-125-050, TU Košice, 1990. [5] NEJMAN L.R., KALANTAROV P.L.: Teoretické základy elektrotechniky, Bratislava,1951. [6] MARTON K.: “Teoretická analýza induktívného snímania čiastkových výbojov”. KTVN, EF TU v Košiciach. [7] MORSHIUS P.H.F.: Partial Discharge Mechanisms, Proefschrift, Delft, 1993. [8] KURIMSKÝ J., KOLCUNOVÁ I., CIMBALA R.: “Understanding surface partial discharges in HV coils and the role of semi-conductive protection”, In: Electrical Engineering (Archiv fur Elektrotechnik): DOI: 10.1007/s00202010-0184-0. Vol. 92, no. 7-8(2010), p. 283289. [9] KURIMSKÝ J., CIMBALA R., KOLCUNOVÁ I. “Multi-scale decomposition for partial discharge analysis”, In: Przeglad Elektrotechniczny. Vol. 84, no. 9 (2008), p. 169-173. - ISSN 0033-2097. [10]DOLNÍK B., KURIMSKÝ J.: “Contribution to earth fault current compensation in middle 18 ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, Nr. 1, ianuarie-martie 2013 voltage distribution networks”, PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 87 NR 2/2011. P. 220224. 7. Biography Jozef BALOGH graduated TU Košice, FEI in 1991. He received the PhD degree in 2001. His research interests concern: partial discharge measurement methods, overvoltage protection and renewable energy exploitation. Jaroslav PETRÁŠ graduated TU Košice, FEI in 1997. He received the PhD degree in 2008. His research interests concern: partial discharge measurement by acoustic methods and renewable energy exploitation.