Electrostatic Synchronous Machine

Figure 2-27 shows a single-phase electrostatic machine. The rotor in this figure has two parallel plates connected electrically to each other and operating best at ground potential. The stator has stationary plates that are interleaved with the rotor plates. An a-c voltage v_a-c is applied between the stator and ground while the stator is rotating at synchronous speed. Since the machine in this illustration has two poles [two lobes shown in Fig. 2-27(a)] the number of revolutions per second is the same as the applied frequency. A machine with p poles has a synchronous speed of

[2-98]

where f= frequency in cycles per second.

Figure 2-27. Electrostatic synchronous machine; (a) end view; (b) cross section.

Let the applied voltage be expressed by

[2-99]

and let the capacitor plates be shaped so that the capacitance between the stator and rotor varies, as follows

[2-100]

From Eq. 2-96 the expression for the developed mechanical power is

[2-101]

Substitution of Eqs. 2-99 and 2-100 in Eq. 2-101 yields

[2-102]

but

hence

[2-103]

which, upon expanding, becomes

[2-104]

Equation 2-104 expresses the instantaneous applied power. The average applied power is

[2-105]

Let σ₀ - θ₀ = θ, then the average applied power is

[2-106]

Electrostatic generators and motors operating on the principles outlined in the preceding pages have very little output for a given size, particularly if they are operating in air at atmospheric pressure because of the low value of dielectric strength at that pressure. However, when operating in a vacuum the rating can be increased considerably because the increased dielectric strength for vacuum allows the applied voltage V to be increased accordingly and the output is proportional to V². Nevertheless, the output of the electrostatic machine, even under ideal conditions, is very small in comparison with that of conventional electromagnetic motors and generators and therefore has limited applications. Since these machines operate in a vacuum they have practically no losses, and since there are no magnetic losses, efficiencies above 99 percent have been realized.