The V-Curves of a Synchronous Motor

The V-Curves of a Synchronous Motor

The magnitude of excitation current affects both the margin of stability and the reactive current of a synchronous motor. Let us analyse this relation by referring to the phasor/vector diagram of a phase of a synchronous motor connected to a large power system

(V = const), as shown in Fig 16. Given a constant retarding torque at the motor shaft, T_ret = T_em its power P = T_emɷ_rot will be likewise constant, so, as follows from Eq. (15.18) and Eq. (15.19), the products

E₀ sin θ = ɷΨ0 sin θ = const

and

I cos φ = I act = const

are always the same and independent of the excitation current. A combined phasor/vector diagram of a phase of a synchronous motor for T_ret = const and for several values of the excitation (field) current I_f = VAr is shown in Fig 17. As I_f (excitation flux. linkage Ψ₀) is reduced, the angle θ increases until the synchron­ous motor loses stability.

As follows from the phasor/vector diagram, the magnitude and effect of the stator current of a synchronous motor

İ = İ_act + İ_reac

depend on the excitation (field) current I_f When the field current is less than some limiting value, I_f < I_f._Iim (P), the stator current I has an inductive reactive component I_reac._L (φ > 0). When the field current exceeds some limiting value, I_f> I_f._Iim , the stator current has a capacitive reactive component I_reac. _c (φ < 0). Hence, in the case of underexcitation the reactive power of a synch­ronous motor is inductive in its effect

Q_L = 3VI_reac, _L

In the case of overexcita­tion, it is capacitive in its effect

Q_C = 3VI_reae. _C

Accordingly, each phase of a synchronous motor connected to a large power system may be represented by an equivalent circuit consisting of a parallel combination of an equivalent resistive element whose resistance depends on the load torque, r = V/I_act = F (T_1oad), and an equivalent inductive (capacitive) element whose inductance (capacitance) is a function of the load torque and the field current:

L = V/ɷI_reac, _L = F (I_f, T_load)

or

C = I_reac. _C/ɷV = F (I_f, T_load)

If the load torque of the motor is zero, T_load = 0, then the equi­valent circuit for a phase of a synchronous motor connected to a large power system will contain no resistive element, and the magnit­ude of the inductive (capacitive) element will be solely dependent on the field current.

The plots relating the stator current or a synchronous motor con­nected to a large power system (V = const) to the field current for a constant load torque, T_load = const, are called the V–curves of the motor (Fig 18).

When no load torque is applied to the shaft of a synchronous motor (T_load = 0), then, on neglecting all forms of loss, it may be deemed that the stator current of a synchronous motor is purely reactive (see Fig 18, P = 0):

İ = İ_reac = (-Ė₀+ V̇)/j = (V̇ + jɷΨ̇₀ ) / j = F(I_f)