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Brief information from the theory
The three-phase system was first created to solve the problem of converting electrical energy into mechanical energy by creating a circular rotating magnetic field. It is widespread due to the simplicity of the three-phase asynchronous motor. The main elements of three-phase circuits are three-phase generator, three-phase transformer, single-phase or three-phase load and connecting wires. A three-phase generating system can be created from three single-phase sources, the EMF of which can be represented by expressions: eA = EAm ∙ sin ω ∙ t; eB = EBm ∙ sin (ω ∙ t + 2400); eC = ECm ∙ sin (ω ∙ t + 1200). In complex form these EDS can be recorded: EA = EAm ∙ e j∙ω t; EB = EBm ∙ e(ϳ∙ω∙t-120˚) ; EC = ECm ∙ e(ϳ∙ω∙t-240 ˚). The time diagram of the three-phase voltage generator is shown in fig. 5.1. Fig. 5.1. The timing diagram of voltages of three-phase generator Most often, the energy systems of industrial, administrative and residential complexes will be implemented according to the star-star scheme with a zero wire, as shown in fig. 5. 2 a, sometimes under the scheme "star" - "star" shown in fig. 5..2 b. There are the following types of three-phase loads. 1. A symmetrical load, which is equal to the complex impedance voltages phase of the receiver: ZA = ZB = ZC = ZA ∙
a
b Fig. 5. 2. Connection scheme of three-phase systems: a ? ?star? - ?star? with zero wire, b ? ?star? - ?star? 1. Uniform load at which the resistance modules of the receiver phases are equal: ZA = ZB = ZC. 2. Uniform load, which is equal to the arguments of the resistance and the phase of the receiver: ⱷA = ⱷB = ⱷC. 3, Asymmetric load at which resistance complexes are not equal in all phases of the receiver: ZA ≠ ZB ≠ ZC. For the ?star? - ?star? scheme with zero wire under arbitrary load, the following relations are valid for the phase current complexes Ia = Ua / Za ; Ib = Ub / Zb ; Ic = Uc / Zc. For neutral current (zero wire): I0 = Ia + Ib + Ic . For linear and phase voltages of the same circuit Ul = At symmetric load, the phase current modules are equal to each other Ia = Ib = Ic = Uph / Zph, and the current in the neutral is zero I0 = 0. For the "star" - "star" schema without neutral for arbitrary load neutral voltage UN = (UA * Ya+ UB ∙ Yb + UC∙ YC) / (Y0 + Ya + Yb + Yc). The voltage on the load phases,, U?a = UA̶ UN ; U?b = UB̶ UN ; U?c = UC̶ UN. The currents in the phases of the load: Ia = U?a / Z? ; Ib= U?b/ Zb ; Ic= U?c/ Zc.. At the same time, in each phase of the circuit, a complex linear currents is equal to the phases current. Il = Iph . Phase shift angles between phase currents and voltages ⱷa = arctg (Xa / Ra); ⱷb = arctg (Xb / Rb); ⱷc = arctg (Xc / Rc), where Ra, Rb, Rc ? resistance of the load phases; Xa, Xb, Xc ? their reaction resistances. Active power of three-phase circuit under arbitrary load P = Pa + Pb + Pc ; reactive power Q = Qa + Qb + Qc ; full power S = With a symmetrical load P = 3 ∙ Uph ∙ Iph ∙ cos ⱷl = Q = 3 ∙ Uph ∙ Iph ∙ sin ⱷl = S = 3 ∙ Uph ∙ Iph = Date: 2018-08-27; view: 28021
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