4.5 Electrostatic Voltmeters
These are used to produced voltages upto 1000KV. It is a voltmeter in which voltage to be measured is applied between fixed and movable metal vanes. The resulting electrostatic force deflects the movable vane against the tension of a spring.
Principle of Operation
In this case force of attraction between two charged surface is used to create a deflection of pointer on scale calibrated in MV. Since the force of attraction is same irrespective of polarity, ESV can be used to measure both DC and AC quantities.
It consists of moving vane NN which is attracted to fixed vane Cs. Moving vane NN is attached to the pointer P and is counter balanced by small weight (or) spring. The voltage applied between these two vanes is equal to the rate of change of stored electrical energy.
It is based on the principle that unlike charges attract when a voltage is applied, moving vanes are drawn so as to be closer to the fixed vanes. When two parallel plates with cross sectional area A and spacing d are charged with q and have a potential difference V then the energy stored in it is given by,
Energy stored = 1/2 CV2 = W (i.e) Energy stored in C = W.D to charge C.
∴ Change in energy = dw = 1/2 V2.dc = F.dx.
The field is produced by the voltage V between a pair of parallel plane disc electrodes, the force F on an area A of the electrode for which the field gradient E is the same across the area and perpendicular to the surface can be calculated from the derivative of the stored electrical energy Wel taken in the field direction (x).
Since each volume element Adx contains the same stored energy,, the attracting force becomes,
—————-(1)
Where, ε = Permittivity of the insulating medium.
S= Gap length between the parallel plane electrodes.
The attracting force is always positive independent of the polarity of the voltage. If the voltage is not constant, the force is also time dependent. Then the mean value of the force is used to measure the voltage, thus
————————(2)
Where T is a proper integration time. Thus electrostatic voltmeters are r.m.s. indicating instruments.
The design of most of the realized instruments is arranged such that one of the electrodes or a part of it is allowed to move. By this movement, the electrical field will slightly change which in general can be neglected.
Besides differences in the construction of the electrode arrangements, the various voltmeters differ in the use of different methods of restoring forces required to balance the electrostatic attraction.
The small movement is generally transmitted and amplified by a spotlight and mirror system but many other systems have also been used. If the movement of the electrode is prevented or minimized and the field distribution can exactly be calculated, the electrostatic measuring device can be used for absolute voltage measurements, since the calibration can be made in terms of the fundamental quantities of length and forces.
The paramount advantage is the extremely low loading effect as only electrical fields have to be built up. The atmospheric air, high-pressure gas or even high vacuum between the electrodes provide very high resistivity and thus the active power losses are mainly due to the resistance of insulating materials used elsewhere.
The measurement of voltages lower than about 50 V is not possible as the forces become too small. The measuring principle displays no upper frequency limit. The load inductance and the electrode system capacitance form a series resonant circuit, thus limiting the frequency range.
For small voltmeters the upper frequency is generally in the order of some MHz. In spite of the inherent advantages of this kind of instrument, their application for high voltage testing purposes is very limited.
For DC voltage measurements, the electrostatic voltmeters compete with resistor voltage dividers or measuring resistors as the very high input impedance is in general not necessary.
For AC voltage measurements, the r.m.s. value is either of minor importance for dielectric testing or capacitor voltage dividers can be used together with low-voltage electronic r.m.s. instruments which provide acceptable low uncertainties.
4.6 Sphere Gaps
Sphere gaps (or) spark gap:
It is used to measure peak value of DC, AC & impulse voltages. Two identical metallic spheres separated by certain distance forms a sphere gap. The gap length between sphere should not exceed the sphere radius.
An uniform spark gap will have a spark over voltage. Hence spark gap can be used to measure peak value of voltage (i.e) if the gap distance is known.
Sphere gap measurements
Sphere gaps can be arranged either as follows:
(i) Vertically with lower sphere grounded.
(ii) Horizontally with both sphere connected to voltage source (or) one sphere grounded.
The two spheres should be identical in size and shape. Voltage to be measured is applied between two spheres and spacing between them gives a measure of the spark over voltage.
A series resistor is connected between source and sphere gap to limit the breakdown current. In order to suppress unwanted oscillations in the source voltage, value of resistance varies from 100 – 1000 Kilo ohms for AC or DC voltage, value of resistance should not exceed 500Ω in case of impulse voltage.
Sphere Gap Construction Assembly
Sphere gaps are made with two metal spheres of identical diameter with shanks, gears and insulator supports. Spheres are made of brass (or) Dl. Standard Diameter of spheres are 2, 5, 6 -20, 10, 12-5, 15, 20, 50, 75, 100, 150 & 200 cm.
Spacing is designed such that flashover occurs near the sparking point P. Sphere should be smooth and curvature is uniform. Radius of curvature is measured using Spherometer.
For small sizes, spheres are placed in horizontal manner whereas in case of large size sphere(large diameter), spheres are placed in vertical manner.
In both cases spacing between spheres should be free from external electric bodies and fields. In order to measure voltage less than 50 Kv (or) to measure high voltage with more accuracy irradiation of gap by other ionising media should be used.
Importance of Irradiation
Statistical time lag is the lag caused by the electron to appear in the gap during the application of voltage. Formative time lag is the time required for the breakdown to develop once initiated.
Both these time lags depends on the irradiation level. If the gap is sufficiently irradiated so that an electron exists in the gap to initiate the spark process. If the gap is subjected to an impulse voltage, breakdown will occur when the peak voltage exceeds the DC breakdown value.
On the other hand the irradiation voltage must be maintained above the breakdown value for a longer time till an electron appears. Irradiation can be done by using radioactive materials, UV illumination by mercury lamps etc.
The time taken by the positive ion to travel from anode to cathode in case of 2° electron emission decides the formative time lag. This time lag voltage increases with gap length for non-uniformity. Resistors are used to limit the current and prevent oscillations in case of power frequency test.
For high frequency voltage drop will increase & it is necessary to have small value R. If the above conditions of the spheres are satisfied, sphere will have spark at a peak V close to nominal value. The standard conditions are at temperature of 20°c and pressure of about 760mm of Mercury.
Sphere Gap
The breakdown strength of gas depends on the ionisation of gas and density of gas. Breakdown voltage varies with gap spacing. By precise experiments, breakdown voltage variation with gap spacing for different diameter & distance have been calculated.
In the measuring device, two metal spheres are used separated by gas gap. Potential difference between spheres is raised until a spark occurs between them. Breakdown strength depends on the size of sphere, distance between them etc. A spark gap can be used for finding peak value of voltage.
Spark over voltage V=Kv0.
Where, K – Correction factor w.r.t δ.
V0 – Spark over Voltage under standard temperature & pressure.
Density of gas (generally air) affects the spark over voltage for a given gap.
P – Air pressure at test condition.
P0 – Air pressure at test condition.
Assume t0 = 20°c, P0 = 760 torr then,
Spark over voltage for a given gap setting under standard conditions (760 torr pressure and 20°c) must be multiplied by the correction factor to obtain actual spark over voltage.
Accuracy of results depends on the ratio of d to D
Where, d → gap spacing and D → Sphere diameter.
If d < 0.5D, Accuracy = ± 3%.
If d < 0.5D, Accuracy = ± 5%.
Breakdown voltage characteristics is dependent on polarity of high voltage sphere in case of asymmetrical gap [(i.e) where one electrode is at high voltage and other at low voltage].
In case of asymmetrical gap, there are two breakdown characteristics. Therefore in sphere gaps to obtain high accuracy in measurement, minimum clearance should be maintained between the spheres and neighboring bodies.
Factors influencing spark over of sphere gaps:
* Nearby earthed objects.
* Atmospheric conditions.
* Influence of humidity.
* Irradiation.
* Polarity & rise time of voltage waveform.
*Switching surges.