High Voltage Engineering PDF

IGIT SARANG HIGH VOLTAGE ENGINEERING (Subject code-PCEE4412) Prepared By Dr. Somashree Pathy Asst. Professor (Consolidated) Electrical Engineering IGIT, Sarang UNIT I GENERATION OF HIGH VOLTAGES AND HIGH CURRENTS  Di...

IGIT SARANG HIGH VOLTAGE ENGINEERING (Subject code-PCEE4412) Prepared By Dr. Somashree Pathy Asst. Professor (Consolidated) Electrical Engineering IGIT, Sarang UNIT I GENERATION OF HIGH VOLTAGES AND HIGH CURRENTS  Different Voltage Level  Rated Voltage  Nominal Voltage Extra-low Voltage Low Voltage Medium voltage High Voltage Extra-High Voltage  In India, mostly porcelain insulators are used for transmitting power. For electrical engg. the main concern of high voltages is for the insulation testing of various components. 3  Necessity: Generation of HV & high current high dc voltages, high ac voltages of power frequency, high ac voltages of high frequency, high transient or impulse voltages of very short duration such as lightning over voltages, and transient voltages of longer duration such as switching surges. Hence, testing of surge diverters or the short-circuit testing of switchgear, high-current testing with several hundreds of amperes is required. Therefore, test facilities require high- voltage and high-current generators. 4  GENERATION OF HIGH D.C VOLTAGE Generation of high d.c. voltages is mainly required in research work in the areas of pure and applied physics. Sometimes, high direct voltages are needed in insulation tests on cables and capacitors. Impulse generator charging units also require high d.c. voltages of about 100 to 200 kV. DIFFERENT METHODS TO GENERATE HIGH D,C VOLTAGE: 1. Half and full wave rectifier circuits 2. Voltage doubler circuits 3. Voltage multiplier circuits 4. Van de Graaff generator HALF AND FULL WAVE RECTIFIER CIRCUITS This method can be used to produce DC voltage up to 20 kV. For high voltages several units can be connected in series. For the first half cycle of the given AC input voltage, capacitor is charged to Vmax and for the next half cycle the capacitor is discharged to the load. The capacitor C is chosen such that the time constant CRl is 10 times that of the AC supply. 5 GENERATION OF HIGH D.C VOLTAGE 6  Ripple Voltage with Half-Wave and Full-Wave Rectifiers When a full-wave or a half-wave rectifier is used along with the smoothing capacitor C, the voltage on no load will be the maximum ac voltage. But when on load, the capacitor gets charged from the supply voltage and discharges into load resistance RL whenever the supply voltage waveform varies from peak value to zero value. These waveforms are shown in Figure. When loaded, a fluctuation in the output dc voltage δV appears, and is called a ripple. 7  Ripple Voltage with Half-Wave and Full-Wave Rectifiers The ripple voltage δV is larger for a half-wave rectifier than that for a full- wave rectifier, since the discharge period in the case of half-wave rectifier is larger. The ripple δV depends on (a) the supply voltage frequency f, (b) the time constant CRL, and (c) the reactance of the supply transformer XL. For half-wave rectifiers, the ripple frequency is equal to the supply frequency and for full-wave rectifiers, it is twice that value. 8 VOLTAGE DOUBLER CIRCUIT In this method, during –ve half cycle, the Capacitor C1is charged through rectifier R to a voltage +Vmax. During next cycle. C1rises to +2Vmax. C2.is charged to 2Vmax. Cascaded voltage doublers can be used for producing larger output voltage 9  Contd… In the voltage doubler circuit shown the capacitor C1 is charged through rectifier R1 to a voltage of +Vmax with polarity as shown in the figure during the negative half cycle. As the voltage of the transformer rises to positive +Vmax during the next half cycle, the potential of the other terminal of C1 rises to a voltage of +2Vmax. Thus, the capacitor C2 in turn is charged through R2 to 2Vmax. Normally, the dc output voltage on load will be less than 2Vmax, depending on the time constant C2RL and the forward charging time constants. The ripple voltage of these circuits will be about 2% for RL/r ≤10 and X/r ≤0.25, where X and r are the reactance and resistance of the input transformer. The rectifiers are rated to a peak inverse voltage of 2Vmax, and the capacitors C1 and C2 must also have the same rating. If the load current is large, the ripple also is more. 10 CASCADED VOLTAGE DOUBLERS Cascaded voltage doublers can be used for producing larger output voltage 11  Contd… The rectifiers R1 and R2 with transformer T1 and capacitors C1 and C2 produce an output voltage of 2V.This circuit is duplicated and connected in series or cascade to obtain a further voltage doubling to 4 V. T is an isolating transformer to give an insulation for 2Vmax since the transformer T2 is at a potential of 2Vmax above the ground. The voltage distribution along the rectifier string R1, R2, R3, and R4 is made uniform by having capacitors C1, C2, C3, and C4 of equal values. The arrangement may be extended to give 6 V, 8 V, and so on, by repeating further stages with suitable isolating transformers. In all the voltage doubler circuits, if valves are used, the filament transformers have to be suitably designed and insulated, as all the cathodes will not be at the same potential from ground. The arrangement becomes cumbersome if more than 4 V is needed with cascaded steps. 12 Contd… 13 VOLTAGE MULTIPLIER CIRCUITS Here n no. of capacitors and diodes are used. Voltage is cascaded to produce output of 2nVmax. Voltage multiplier circuit using Cockcroft- Walton principle can be used. 14 Contd… 15  Contd… Therefore, the use of several stages arranged in this manner enables very high voltages to be obtained. The equal stress of the elements used is very convenient and promotes a modular design of such generators. The number of stages, however, is strongly limited by the current due to any load. This can only be demonstrated by calculations, even if ideal rectifiers, capacitors and an ideal a.c. voltage source are assumed. The a.c. voltage source V(t) is usually provided by an h.v. transformer, if every stage is built for high voltages, typically upto about 300 kV. The voltage waveform does not have to be sinusoidal: every symmetrical waveform with equal positive and negative peak values will give good performance. As often high-frequency input voltages are used, this hint is worth remembering. 16  Cockroft –Walton Voltage multiplier circuit… The first stage, i.e., D1, D2, C1, C2, and the transformer T are identical as in the voltage doubler circuit. For higher output voltage of 4, 6,... 2n of the input voltage V, the circuit is repeated with cascade or series connection. Thus, the capacitor C4 is charged to 4Vmax and C2n to 2nVmax above the earth potential. But the voltage across any individual capacitor or rectifier is only 2Vmax. 17 Contd… 18  Generator loaded Condition When the generator is loaded, the output voltage will never reach the value 2n Vmax. Also, the output wave will consist of ripples on the voltage. Thus, we have to deal with two quantities, the voltage drop ΔV and the ripple δV. Suppose a charge q is transferred to the load per cycle. This charge is q = I/f = IT. The charge comes from the smoothening column, the series connection of C′1, C′2, C′3. If no charge were transferred during T from this stack via D1, D2, D3, to the oscillating column, the peak to peak ripple would merely be 19  Contd… The second quantity to be evaluated is the voltage drop ΔV which is the difference between the theoretical no load voltage 2nVmax and the onload voltage. Here C1′ is not charged upto full voltage 2Vmax but only to 2Vmax – 3q/C because of the charge given up through C1 in one cycle which gives a voltage drop of 3q/C = 3I/fC 20 Contd… 21  Contd… Here again the lowest capacitors contribute most to the voltage drop ΔV and so it is advantageous to increase their capacitance in suitable steps. However, only a doubling of C1 is convenient as this capacitors has to withstand only half of the voltage of other capacitors. Therefore, ΔV1 decreases by an amount nI/fC which reduces ΔV of every stage by the same amount. The optimum number of stages assuming a constant Vmax, I, f and C can be obtained as The maximum output voltage (V0max)max 22  Contd… The rectifiers D1, D3,...D2n-1 operate and conduct during the positive half cycles while the rectifiers D2, D4...D2n conduct during the negative half cycles. The voltage on C2 is the sum of the input ac voltage,Vac and the voltage across condenser VC1 as shown in figure. The mean voltage on C2 is less than the positive peak charging voltage (Vac+VC1).The voltage across other capacitors C2 to C2n can be derived in the same manner (i.e.) from the difference between voltage across the previous capacitor and the charging voltage. Finally, the voltage after 2n stages will be Vac (n1 + n2 +...), where n1, n2,... are factors when ripple and regulation are considered in the next rectifier. The ripple voltage δV and the voltage drop ΔV in a cascaded voltage multiplier unit are shown in Figure. 23  Contd… Voltage waveforms across the first and the last capacitors of the cascaded voltage multiplier circuit 24  Electrostatic generator Electrostatic generators convert mechanical energy into electric energy directly. The electric charges are moved against the force of electric fields, thereby higher potential energy is gained at the cost of mechanical energy. The basic principle of operation is explained in the given figure. In the figure an insulated belt is moving with uniform velocity ν in an electric field of strength E (x). Assuming the width of the belt is b and the charge density ζ consider a length dx of the belt, the charge dq = ζ bdx. 25  Contd… The force experienced by this charge (or the force experienced by the belt). dF = Edq = E ζ bdx or F = ζb∫Edx Normally the electric field is uniform ∴ F = ζbV The power required to move the belt = Force × Velocity= Fv = ζbVν Now current I = (dq/dt) = ζb*(dx/dt)=ζbv ∴ The power required to move the belt P = Fν = ζbVν = VI Assuming no losses, the power output is equal to VI. 26  VAN DE GRAFF GENERATOR The generator is usually enclosed in an earthed metallic cylindrical vessel and is operated under pressure or in vacuum. An insulating belt is run over pulleys. The belt, the width of which may vary from a few cms to metres is driven at a speed of about 15 to 30 m/sec, by means of a motor connected to the lower pulley. 27  Contd… The belt near the lower pulley is charged electrostatically by an excitation arrangement. The lower charge spray unit consists of a number of needles connected to the controllable d.c. source (10 kV–100 kV) so that the discharge between the points and the belt is maintained. The charge is conveyed to the upper end where it is collected from the belt by discharging points connected to the inside of an insulated metal electrode through which the belt passes. The entire equipment is enclosed in an earthed metal tank filled with insulating gases of good dielectric strength. So that the potential of the electrode could be raised to relatively higher voltage without corona discharges or for a certain voltage a smaller size of the equipment will result. 28  Contd… The shape of the h.t., electrode should be such that the surface gradient of electric field is made uniform to reduce again corona discharges, even though it is desirable to avoid corona entirely. An isolated sphere is the most favourable electrode shape and will maintain a uniform field E with a voltage of Er where r is the radius of the sphere. As the h.t. electrode collects charges its potential rises. The potential at any instant is given as V = q/C where q is the charge were collected at that instant. It appears as though if the charge were collected for a long time any amount of voltage could be generated. 29  Contd… As the potential of electrode rises, the field set up by the electrode increases and that may ionise the surrounding medium and, therefore, this would be the limiting value of the voltage. In practice, equilibrium is established at a terminal voltage which is such that the charging current I =C(dV/dt) equals the discharge current which will include the load current and the leakage and corona loss currents. The moving belt system also distorts the electric field and, therefore, it is placed within properly shaped field grading rings. The grading is provided by resistors and additional corona discharge elements. 30  Contd… In order to have a rough estimate of the current supplied by the generator, let us assume that the electric field E is normal to the belt and is homogeneous. We know that D = ε0 E where D is the flux density and since the medium surrounding the h.t. terminal is say air εr = 1 and ε0 = 8.854 × 10–12 F/metre. According to Gauss law, D = ζ the surface charge density. Therefore, D = ζ = ε0 E Assuming E = 30 kV/cm or 30,000 kV/m ζ = 8.854 × 10–12 × 3000 × 103 = 26.562 × 10–6 C/m2 Assuming for a typical system b = 1 metre and velocity of the belt ν = 10 m/sec, and using equation (I = ζ bν), the current supplied by the generator is given as I = ζ bν = 26.562 × 10–6 × 1 × 10 = 26.562 × 10–5 Amp = 265 μA 31 Contd… The advantages of the generator are: (i) Very high voltages can be easily generated (ii) Ripple free output (iii) Precision and flexibility of control The disadvantages are: (i) Low current output (ii) Limitations on belt velocity due to its tendency for vibration. The vibrations may make it difficult to have an accurate grading of electric fields Uses These generators are used in nuclear physics laboratories for particle acceleration and other processes in research work. 32  GENERATION OF HIGH ALTERNETING VOLTAGES Applicable for low power high voltage testing for short time on high voltage equipment. Cuurent for different hv equipments are: Insulation. C.B, instrument, transformer :0.1A-0.5A Power transformer, HV capacitors: 0.5A-1A Cables: 1A & above Flux density is lowered to have reduced magnetising current which removes saturation of the core such that harmonics can be removed. Series connection of the several units of transformers used to produce very high voltage. 33 CASCADE TRANSFORMERS 34  Contd... The weight of the whole unit is subdivided into single units and, therefore, transport and erection becomes easier. Also, with this, the transformer cost for a given voltage may be reduced, since cascaded units need not individually possess the expensive and heavy insulation required in single stage transformers for high voltages exceeding 345 kV. As cost of insulation for a single unit is proportional to square of operating voltage. Figure shows a basic scheme for cascading of three transformers. The primary of the first stage transformer is connected to a low voltage supply. A voltage is available across the secondary of this transformer. The tertiary winding (excitation winding) of first stage has the same number of turns as the primary winding, and feeds the primary of the second stage transformer. 35  Contd... The potential of the tertiary is fixed to the potential V of the secondary winding as shown in Figure. The secondary winding of the second stage transformer is connected in series with the secondary winding of the first stage transformer, so that a voltage of 2V is available between the ground and the terminal of secondary of the second stage transformer. Similarly, the stage-III transformer is connected in series with the second stage transformer. With this the output voltage between ground and the third stage transformer, secondary is 3V. Individual stages except the upper most must have three-winding transformers. The upper most, however, will be a two winding transformer. Figure shows metal tank construction of transformers and the secondary winding is not divided. Here the low voltage terminal of the secondary winding is connected to the tank. The tank of stage-I transformer is earthed. The tanks of stage-II and stage-III transformers have potentials of V and 2V, respectively above earth ed. Through h.t. bushings, the leads from the tertiary winding and the h.v. winding are brought out to be connected to the next stage 36 transformer.  Contd… Disadvantage: the lower stage transformer of the primaries of the transformers are loaded more as compared with the upper stages. The loading of various windings is indicated by P in figure For the three-stage transformer, the total output VA will be 3VI = 3P and, therefore, each of the secondary winding of the transformer would carry a current of I = P/V. The primary winding of stage-III transformer is loaded with P and so also the tertiary winding of second stage transformer. Therefore, the primary of the second stage transformer would be loaded with 2P. Extending the same logic, it is found that the first stage primary would be loaded with P. Therefore, while designing the primaries and tertiaries of these transformers, this factor must be taken into consideration. 37  Contd... The total short circuit impedance of a cascaded transformer from data for individual stages can be obtained. The equivalent circuit of an individual stage is shown in Figure. Here Zp, Zs, and Zt, are the impedances associated with each winding. The impedances are shown in series with an ideal 3-winding transformer with corresponding number of turns Np, Ns and Nt. The impedances are obtained either from calculated or experimentally-derived results of the three shortcircuit tests between any two windings taken at a time. 38  Contd... For an n-stage transformer, Where Xpi, Xsi and Xti are the short-circuit reactance of the primary, secondary and tertiary windings of ith transformer. Impedance of a II-stage transformer is about 3–4 times the impedance of one unit and a III-stage impedance is 8–9 times the impedance of one unit transformer. Hence, in order to have a low impedance of a cascaded transformer, it is desirable that the impedance of individual units should be as small as possible. 39  Contd… Testing of an hv apparatus or insulation always involves supplying of capacitive loads with very low power dissipation. Thus if C is the capacitance of the test object, V is the rms value of the nominal output voltage of the transformer at an angular frequency ω then the nominal rating of the transformer in kVA will be P = K. v2 ωC, where K (> 1.0) is a factor to account for any extra capacitance in the test circuit like that of the measuring capacitance divider, etc. K may have values of the order of 2 or more for very high voltages (> 1 MV). 40  Contd… Typical capacitance values for high capacitance test objects like power transformers, cables, etc. are as follows: 41  Contd… Power Supply for ac Test Circuits Large cascade transformers units are supplied power through a separate motor-generator set or by means of voltage regulators. Supply through a voltage regulator will be cheaper, and will be more flexible in the sense that the units in the cascade set can be operated in cascade, or in parallel, or as three-phase units. It is also necessary that the impedance of the voltage regulating transformer is low in all voltage positions, from the minimum to the rated value. 42  Resonant Transformers The equivalent circuit of a high-voltage testing transformer consists of the leakage reactance of the windings, the winding resistances, the magnetizing reactance, and the shunt capacitance across the output terminal as shown in the figure. Transformer Equivalent Transformer Ckt 43  Contd… It may be seen that it is possible to have series resonance at power frequency ω, if (L1 +L2) = 1/ωC. With this condition, the current in the test object is very large and is limited only by the resistance of the circuit. Usually the load capacitance is variable and it is possible that for certain loading, resonance may occur in the circuit suddenly and the current will then only be limited by the resistance of the circuit and the voltage across the test specimen may go up as high as 20 to 40 times the desired value. The magnitude of the voltage across the capacitance C of the test object will be 44  Contd… This is called as the Q- factor of the circuit and gives the magnitude of the voltage multiplication across the test object under resonance conditions. Therefore, the input voltage required for excitation is reduced by a factor l/Q, and the output kVA required is also reduced by a factor l/Q. The secondary power factor of the circuit is unity. This principle is utilized in testing at very high voltages and on occasions requiring large current outputs such as cable testing, dielectric loss measurements, partial discharge measurements, etc. The test condition is set such that (ω(Le+L)) = 1/ωC where Le is the total equivalent leakage inductance of the transformer including its regulating transformer. 45  Contd The chief advantages of this principle are (a) it gives an output of pure sine wave, (b) power requirements are less (5 to l0% of total kVA required), (c) no high-power arcing and heavy current surges occur if the test object fails, as resonance ceases at the failure of the test object, (d) cascading is also possible for very high voltages, (e) simple and compact test arrangement, and (f) no repeated flashovers occur in case of partial failures of the test object and insulation recovery. The disadvantages are the requirements of additional variable chokes capable of withstanding the full test voltage and the full current rating. 46  GENERATION OF IMPULSE VOLTAGES An impulse voltage is a unidirectional voltage which, without appreciable oscillations, rises rapidly to a maximum value and falls more or less rapidly to zero. If an impulse voltage develops without causing flash over or puncture, it is called a full impulse voltage; if flash over or puncture occur, thus causing a sudden collapse of the impulse voltage, it is called a chopped impulse voltage. A full impulse voltage is characterized by its peak value and its two-time intervals, the wave front and wave tail time intervals. Wave tail time 47  Contd… The wave front time of an impulse wave is the time taken by the wave to reach to its maximum value starting from zero value. Usually it is difficult to identify the start and peak points of the wave and, therefore, the wave front time is specified as 1.25 times (t2 – t1), where t2 is the time for the wave to reach to its 90% of the peak value and t1 is the time to reach 10% of the peak value. Since (t2 – t1) represents about 80% of the wave front time, it is multiplied by 1.25 to give total wave front time. The point where the line CA intersects the time axis is referred to be the nominal starting point of the wave. The nominal wave tail time is measured between the nominal starting point t0 and the point on the wave tail where the voltage is 50% of the peak value i.e. wave fail time is expressed as (t3 – t0). 48  Chopped Wave The nominal steepness of the wave front is the average rate of rise of voltage between the points on the wave front where the voltage is 10% and 90% of the peak value respectively. If chopping takes place on the front part of the wave, it is known as front chopped wave, else, a chopped wave, Again, if chopping takes place on the front, it is specified by the peak value corresponding to the chopped value and its nominal steepness is the rate of rise of voltage measured between the points where the voltage is 10% and 90% respectively of the voltage at the instant of chopping. 49  Impulse Flash Over Voltage Whenever an impulse voltage is applied to an insulating medium of certain thickness, flash over may or may not take place. However, it is to be noted that the flash over occurs at an instant after the attainment of the peak value. The flash over also depends upon the polarity, duration of wave front and wave tails of the applied impulse voltages. If the flash over occurs more than 50% of the number of applications, it is defined as impulse flash over voltage in excess of 50%. The impulse flash over voltage for flash over on the wave front is the value of the impulse voltage at the instant of flash over on the wave front. The impulse ratio for flash over is the ratio of impulse flash over voltage to the peak value of power frequency flash over voltage. Impulse Puncture Voltage: it is the peak value of the impulse voltage which causes puncture of the material when puncture occurs on the wave tail and is the value of the voltage at the instant of puncture when puncture occurs on the wave front. The impulse ratio for puncture is the ratio of the impulse puncture voltage to the peak value of the power frequency puncture voltage. 50  Impulse generator circuit Exact equivalent circuit single stage impulse generator with a typical load : C1 is the capacitance of the generator charged from a d.c. source to a suitable voltage which causes discharge through the sphere gap. The capacitance C1 may consist of a single capacitance, in which case the generator is known as a single stage generator or alternatively if C1 is the total capacitance of a group of capacitors charged in parallel and then discharged in series, it is then known as a multistage generator. 51  Contd... L1 is the inductance of the generator usually kept small. The resistance R1 consists of the inherent series resistance of the capacitances and leads and often includes additional lumped resistance inserted within the generator for damping purposes and for output waveform control. L3, R3 are the external elements which may be connected at the generator terminal for waveform control. R2 and R4 control the duration of the wave. However, R4 also serves as a potential divider when a CRO is used for measurement purposes. C2 and C4 represent the capacitances to earth of the high voltage components and leads. C4 also includes the capacitance of the test object and of any other load capacitance required for producing the required wave shape. 52  Contd... L4 represents the inductance of the test object and may also affect the wave shape appreciably. Usually for practical reasons, one terminal of the impulse generator is solidly grounded. The polarity of the output voltage can be changed by changing the polarity of the d.c. charging voltage. Two simplified but more practical forms of impulse generator circuits are The two circuits are widely used and differ only in the position of the wave tail control resistance R2. When R2 is on the load side of R1 (Fig. a) the two resistances form a potential divider which reduces the output voltage but when R2 is on the generator side of R1 (Fig. b) this particular loss of output voltage is absent. 53  Contd... The impulse capacitor C1 is charged through a charging resistance (not shown) to a d.c. voltage V0 and then discharged by flashing over the switching gap with a pulse of suitable value. The desired impulse voltage appears across the load capacitance C2. The value of the circuit elements determines the shape of the output impulse voltage. The following analysis will help us in evaluating the circuit parameters for achieving a particular wave shape of the impulse voltage. 54  Analysis of Circuit ‘a’ After the gap sparks over, let the current in the generator circuit be i (t) at any time t. Using Laplace transform, the impedance of the circuit is and 55 Contd… vs 56  Contd… Finding the partial fractions of the expression After solving we found So v(t) 57  Contd… Let t1 be the wave front time and t2 the wave tail time, then both α and β must have unique values irrespective of the particular circuit used. At time t1, the shope of the wave is zero, therefore, t1 can be obtained from the relation dv(t)/dt = 0. Peak value of the voltage is then given by 58  Contd… Similarly, t2 can be obtained by substituting t = t2 in v(t) equation and the voltage is half of what it is when t = t1 in the same equation i.e. By simplifying If 2βt1 > 4 then 59  Contd… From the circuit analysis the values of R1 and R2 are found. It shows hat for a given wave shape (certain value of α and β) resistance R2 depends upon the ratio γ(Where γ=C1/C2). Similarly, value of R1 can also be derived to be and This shows that in order to realise a given wave shape, certain values of R1 and R2 are required and these values will depend upon the ratio C1/C2. In order that R1 and R2 are physically realisable resistance, the ratio C1/C2 must not exceed certain value. This ratio can be evaluated for different wave shapes by choosing the typical values of α and β. 60  MULTISTAGE IMPULSE GENERATOR CIRCUIT In order to obtain higher impulse voltage, a single stage circuit is inconvenient for the following reasons: (i) The physical size of the circuit elements becomes very large. (ii) High d.c. charging voltage is required. (iii) Suppression of corona discharges from the structure and leads during the charging period is difficult. (iv) Switching of very high voltages with spark gaps is difficult. In 1923 E. Marx suggested a multiplier circuit which is commonly used to obtain impulse voltages with as high a peak value as possible for a given d.c. charging voltage. A single capacitor C1 may be used for voltages up to 200 kV. Beyond this voltage, a single capacitor and its charging unit may be too costly, and the size becomes very large. The cost and size of the impulse generator increases at a rate of the square or cube of the voltage rating. Hence, for producing very high voltages, 61 a bank of capacitors are charged in parallel and then discharged in series.  MARX CIRCUIT Depending upon the charging voltage available and the output voltage required a number of identical impulse capacitors are charged in parallel and then discharged in series, thus obtaining a multiplied total charging voltage corresponding to the number of stages. Equivalent Marx circuit 62  Contd… Usually the charging resistance Rs is chosen to limit the charging current to about 50 to 100 mA, and the generator capacitance C is chosen such that the product CRs is about 10 s to 1 min. The gap spacing is chosen such that the breakdown voltage of the gap G is greater than the charging voltage V. Thus, all the capacitances are charged to the voltage V in about 1 minute. When the impulse generator is to be discharged, the gaps G are made to spark over simultaneously by some external means. Thus, all the capacitors C get connected in series and discharge into the load capacitance or the test object. The discharge time constant CR1/n (for n stages) will be very very small (microseconds), compared to the charging time constant CRs which will be few seconds. Hence, no discharge takes place through the charging resistors Rs. 63  Modified MARX Circuit In the modified Marx circuit the resistances R1 and R2 are incorporated inside the unit. R1 is divided into n parts equal to R1/n and put in series with the gap G. R2 is also divided into n parts and arranged across each capacitor unit after the gap G. This arrangement saves space, and also the cost is reduced. But, in case the wave shape is to be varied widely, the variation becomes difficult. The additional advantages gained by distributing R1 and R2 inside the unit are that the control resistors are smaller in size and the efficiency (V0ZnV) is high. 64  Contd… Impulse generators are nominally rated by the total voltage (nominal), the number of stages, and the gross energy stored. The nominal output voltage is the number of stages multiplied by the charging voltage. The nominal energy stored is given by ½(C1V2) where C1 = C/n (the discharge capacitance) and V is the nominal maximum voltage (n times charging voltage). In order that the Marx circuit operates consistently it is essential to adjust the distances between various sphere gaps such that the first gap G1 is only slightly less than that of G2 and so on. If is also necessary that the axes of the gaps G be in the same vertical plane so that the ultraviolet radiations due to spark in the first gap G, will irradiate the other gaps. This ensures a supply of electrons released from the gap electrons to initiate breakdown during the short period when the gaps are subjected to over voltages. 65  Components of a Multistage Impulse Generator (i) dc Charging Set The charging unit should be capable of giving a variable dc voltage of either polarity to charge the generator capacitors to the required value. (ii) Charging Resistors These will be non-inductive high value resistors of about 10 to 100 kiloohms. Each resistor will be designed to have a maximum voltage between 50 and 100 kV. (iii) Generator Capacitors and Spark Gaps These are arranged vertically one over the other with all the spark gaps aligned. The capacitors are designed for several charging and discharging operations. On dead short circuit, the capacitors will be capable of giving 10 kA of current. The spark gaps will be usually spheres or hemispheres of 10 to 25 cm diameter. Sometimes spherical ended cylinders with a central support may also be used. (iv) Wave-shaping Resistors and Capacitors Resistors will be non-inductive wound type and should be capable of discharging impulse currents of 1000 A or more. Each resistor will be designed for a maximum voltage of 50 to 100 kV The resistances are bifilar wound on non-inductive thin flat insulating sheets. In some cases, they are wound on thin cylindrical formers and are completely enclosed. The load capacitor 66 may be of compressed gas or oil filled with a capacitance of 1 to 10 nF.  Contd… (v) Triggering System This consists of trigger spark gaps to cause spark breakdown of the gaps (vi) Voltage Dividers Voltage dividers of either damped capacitor or resistor type and an oscilloscope with recording arrangement are provided for measurement of the voltages across the test object. Sometimes a sphere gap is also provided for calibration purposes. (vii) Gas Insulated Impulse Generators Impulse generators rated for 4 MV or above will be very tall and require large space. As such they are usually located in open space and are housed in an insulated enclosure. The height of a 4.8 MV unit may be around 30 m. To make the unit compact, a compressed gas, such as N2 or SF6 may be used as the insulation. Impulse generators are needed to generate very fast transients having time duration of 0.5/5 or 0.1/1.0 μs waves for testing Gas Insulated Systems (GIS) that are coming up nowadays. The energy needed for testing of this type of equipment is small (less than 30 kJ) and the load capacitance is usually less than 500 pF. 67  IMPULSE CURRENT GENERATION The impulse current wave is specified on the similar lines as an impulse voltage wave. 68  Contd… High current impulse generators usually consist of a large number of capacitors connected in parallel to the common discharge path. capacitance C charged to a voltage V0 which can be considered to discharge through an inductance L and a resistance R. In practice both L and R are the effective inductance and resistance of the leads, capacitors and the test objects. 69  Circuit Analysis After the gap S is triggered, the Laplace transform current is given as Where 70  Contd… For current i(t) to be maximum di (t)/dt = 0 After solving where tmax is the time when the first maximum value of current occurs and 71  Contd… Substituting the value of t = tmax the maximum value of current is given as Where the initial energy stored by the generator. If R = 0, ν = 0 then I = V0 (C/ L)1/2 and 72  TRIPPING AND CONTROL OF IMPULSE GENERATORS In large impulse generators, the spark gaps are generally sphere gaps or gaps formed by hemispherical electrodes. The gaps are arranged such that sparking of one gap results in automatic sparking of other gaps as overvoltage is impressed on the other. A simple method of controlled tripping consists of making the first gap a three electrode gap and firing it from a controlled source. 73  TRIPPING AND CONTROL OF IMPULSE GENERATORS The first stage of the impulse generator is fitted with a three electrode gap, and the central electrode is maintained at a potential in between that of the top and the bottom electrodes with the resistors R1 and R1. The tripping is initiated by applying a pulse to the thyratron G by closing the switch S. C produces an exponentially decaying pulse of positive polarity. The pulse goes and initiates the oscilloscope time base. The Thyratron conducts on receiving the pulse from the switch S and produces a negative pulse through the capacitance C1 at central electrode. Voltage between central electrode and the top electrode goes above its sparking potential and hence the gap conducts. 74 Contd… Multistage Generator Control unit 75  TRIPPING CIRCUIT USING A TRIGATRON The three-electrode gap requires larger space and an elaborate construction. Nowadays a trigatron gap is used, and this requires much smaller voltage for operation compared to the three- electrode gap. A trigatron gap consists of a high voltage spherical electrode, an earthed main electrode of spherical shape, and a trigger electrode through the main electrode. Tripping of the impulse generator is effected by a trip pulse which produces a spark between the trigger electrode and the earthed sphere. Due to space charge effects and distortion of the field in the main gap, spark over of the main gap occurs. The trigatron gap is polarity sensitive and a proper polarity pulse should be applied for correct operation. 76  Contd… A trigatron gap which is used as the first gap of the impulse generator and consists essentially of a three-electrode gap. The high voltage electrode is a sphere and the earthed electrode may be a sphere, a semi-sphere or any other configuration which gives homogeneous electric field. A small hole is drilled into the earthed Trigatron gap electrode into which a metal rod projects. The annular gap between the rod and the surrounding hemisphere is about 1 mm. A glass tube is fitted over the rod electrode and is surrounded by a metal foil which is connected to the earthed hemisphere. 77  Contd… The metal rod or trigger electrode forms the third electrode, being essentially at the same potential as the drilled electrode, as it is connected to it through a high resistance, so that the control or tripping pulse can be applied between these two electrodes. When a tripping pulse is applied to the rod, the field is distorted in the main gap and the latter breaks down at a voltage appreciably Trigatron gap lower than that required to cause its breakdown in the absence of the tripping pulse. The function of the glass tube is to promote corona discharge round the rod as this causes photoionisation in the annular gap and the main gap and consequently facilitates their 78 rapid breakdown.  GENERATION OF HIGH FREQUENCY A.C HIGH VOLTAGES For testing electrical apparatus for switching surges, high frequency high voltage damped oscillations are needed which need high-voltage high-frequency transformers. The advantages of these high-frequency transformers are: (i) the absence of iron core in transformers and hence saving in cost and size, (ii) pure sine-wave output, (iii) slow build-up of voltage over a few cycles and hence no damage due to switching surges, and (iv) uniform distribution of voltage across the winding coils due to subdivision of coil stack into a number of units. 79  Contd… High frequency high voltage damped oscillations are needed which need high voltage high frequency transformer which is a Tesla coil. Tesla coil is a doubly tuned resonant circuit, having primary voltage rating 10 kV and secondary voltage rated from 500 to 1000 kV. The primary is fed from DC or AC supply through C1.A spark gap G connected across the primary is triggered at V1 which induces a high self excitation in the secondary.The windings are tuned to a frequency of 10 to 100 kHz. 80  Contd… The primary is fed from a dc or ac supply through the capacitor C1. A spark gap G connected across the primary is triggered at the desired voltage V1 which induces a high self-excitation in the secondary. The primary and the secondary windings (L1 and L2) are wound on an insulated former with no core (air-cored) and are immersed in oil. The windings are tuned to a frequency of 10 to 100 kHz by means of the capacitors C1 and C2. 81  Contd… The primary coil is wound on an insulator fibre tube of about 1 m length to represent a cylindrical or helical winding and consists of a few tens of turns (usually copper strip or tubings). The secondary winding is spaced quite away from the primary winding on another concentric fibre or pyrex tube with a few thousand turns. The whole assembly will be immersed in an oil tank under pressure. With separate bushings taken out for the primary and the secondary windings, the primary winding is supplied through a high-voltage capacitor rectifier unit rated for 10 kV to 50 kV or more and the power rating of the transformer may be 10 kVA or more. The output voltage V2 is a function of the parameters L1,L2, C1, C2, and the mutual inductance M. Usually, the winding resistances will be small and contribute only for damping of the oscillations. 82  Contd… The analysis of the output waveform can be done in a simple manner neglecting the winding resistances. Let the capacitor C1 be charged to a voltage Vl when the spark gap is triggered. Let a current il flow through the primary winding L1 and produce a current i2 through L2 and C2. If W1 is the energy stored in C1 and W2 is the energy transferred to C2 and if the efficiency of the transformer is η, then It can be shown that if the coefficient of coupling K is large the oscillation frequency is less, and for large values of the winding resistances and K, the waveform may become a unidirectional impulse. 83  Problem A 100 kVA, 400 V/250 kV testing transformer has 8% leakage reactance and 2% resistance on 100 kVA base. A cable has to be tested at 500 kV using the above transformer as a resonant transformer at 50 Hz. If the charging current of the cable at 500 kV is 0.4 A, find the series inductance required. Assume 2% resistance for the inductor to be used and the connecting leads. Neglect dielectric loss of the cable. What will be the input voltage to the transformer? 84